Minimum variance

The use of futures contracts as a hedging instrument has been the focus of much research. At the theoretical level, an optimal hedge strategy is traditionally based on the expected-utility maximization paradigm. A simplification of this paradigm leads to the minimum-variance criterion. Although this paradigm is quite well accepted, alternative approaches have been sought. At the empirical level, research on futures hedging has benefited from the recent developments in the econometrics literature. Much research has been done on improving the estimation of the optimal hedge ratio. As more is known about the statistical properties of financial time series, more sophisticated estimation methods are proposed. In this survey we review some recent developments in futures hedging. We delineate the theoretical underpinning of various methods and discuss the econometric implementation of the methods. . Of course, we are solely responsible for any omissions and commissions.

This paper presents an empirical comparison of the out of sample hedging performance from naïve and minimum variance hedge ratios for the four largest US index exchange traded funds (ETFs). Efficient hedging is important to offset long and short positions on market maker's accounts, particularly imbalances in net creation or redemption demands around the time of dividend payments. Our evaluation of out of sample hedging performance includes aversion to negative skewness and excess kurtosis. The results should be of interest to hedge funds employing tax arbitrage or leveraged long-short equity strategies as well as to ETF market makers.

With institutional investors increasingly involved in alternative investments, portfolio optimisation within a large universe of hedge funds has become a key area for research. This paper develops a portfolio construction model that is specifically designed for funds of hedge funds, incorporating specific controls for operational limitations, data biases and incompleteness. Absolute performance is targeted by selecting funds according to their

This empirical study examines the impact of both advanced electronic trading platforms and index exchange traded funds (ETFs) on the minimum variance hedging of stock indices with futures. Our findings show that minimum variance hedging may provide an out-of-sample hedging performance that is superior to that of the naïve futures hedge, but only in markets without active trading of ETFs and advanced development of electronic communications networks. However there is no evidence to suggest that complex econometric models that include, for instance, time varying conditional covariances and error correction can improve on the simple ordinary least squares hedge ratio. Furthermore, in markets with actively traded index ETFs and where electronic trading has become established, no significant efficiency gains are apparent from any minimum variance hedge.

Beamspace methods are applied to EEG/MEG source localization problems in this paper. Beamspace processing involves passing the data through a linear transformation that reduces the data dimension prior to applying a desired statistical signal processing algorithm. This process generally reduces the data requirements of the subsequent algorithm. We present one approach for designing beamspace transformations that are optimized to preserve source activity located within a given region of interest and show that substantial reductions in dimension are obtained with negligible signal loss. Beamspace versions of maximum likelihood dipole fitting, MUSIC, and minimum variance beamforming source localization algorithms are presented. The performance improvement offered by the beamspace approach with limited data is demonstrated by bootstrapping somatosensory data to evaluate the variability of the source location estimates obtained with each algorithm. The quantitative benefits of beamspace processing depend on the algorithm, signal to noise ratio, and amount of data. Dramatic performance improvements are obtained in scenarios with low signal to noise ratio and a small number of independent data samples.

This paper investigates the optimal short-term hedging of Exchange Traded Fund (ETF) portfolios with index futures. Using daily data from May 2000 to December 2004 on the four largest passive ETFs (the Spider, the Diamond, the Cubes and the Russell iShare) and their corresponding index futures we examine the performance of minimum variance hedges for efficient variance reduction and for investors with exponential utility. Our findings relate to daily hedging based on OLS regression, exponentially weighted moving averages and ECM-GARCH models and the utility-based performance evaluation criterion is adopted to capture an efficient reduction in skewness and kurtosis as well as the variance. The basis risk on US equity indices is now extremely low and as a result we find no evidence that minimum variance hedge ratios outperform a naïve 1:1 futures hedge, either for individual ETFs or for portfolios of ETFs.

This paper provides an empirical study of the effectiveness of hedging the spider, a passive exchange traded fund (ETF) that replicates the S&P500 index. The spider is by far the largest ETF in the world: trading on the spider has grown so much during the past few years that it is now amongst the few most traded securities in the AMEX. The large net daily creation and redemption orders of recent years pose a problem to the market makers in the spider, as the orders may be too large to execute in the cash market. They face a decision about whether to hedge spider positions on their own book; and if so, how should they hedge? We have employed several sophisticated minimum variance estimates for the future hedge ratio, including OLS regression, an ECM to account for maturity effects and the cointegration of the spot and the future prices and, to the ECM residuals we apply EWMA and number of bivariate GARCH models to account for timevariation in the hedge ratio. We have applied these models to daily data for a 1-day rebalancing frequency and to weekly data for a 5-day re-balancing frequency, using data since the spider's inception until the end of 2004. Marginal differences in the 'optimal' hedge ratios are apparent, but they are simply too small to have any significant effect on the hedged portfolio volatility. In out-ofsample testing we find that the naïve hedge where an equal and opposite position is taken in the future performs as well as the more technically sophisticated models, at both the daily and the weekly re-balancing frequency. Finally, we have considered the differences between hedging the spot index and hedging the spider. The efficiency of hedging the spider is superior to that of the index and the spider hedged portfolios have significantly lower volatility than the spot index hedged portfolios.

We present a portfolio model of financial intermediation in which currency choice is determined by hedging decisions on both sides of a bank's balance sheet. We show that minimum variance portfolio (MVP) allocations provide a natural benchmark to estimate the scope for dollarization of assets and liabilities (financial dollarization) as a function of macroeconomic uncertainty. Within this benchmark, we find that financial dollarization displays high persistence whenever the expected volatility of the inflation rate remains high in relation to that of the real exchange rate, even after price stabilization has been achieved. The empirical evidence confirms that MVP dollarization approximates financial dollarization closely for a broad sample of countries. 

We propose a simple procedure for the real-time estimation of the average rainfall over a catchment area. The rainfall is modeled as a two-dimensional random field. The average areal rainfall is computed by a linear unbiased minimum variance estimation method (kriging) which requires knowledge of the variogram of the random field. We propose a time-varying estimator for the variogram which takes into account the influences of both the seasonal variations and the rainfall intensity. Our average areal rainfall estimator has been implemented in practice. We illustrate its application to real data in two river basins in Belgium. Finally, it is shown how the method can be used for the optimal selection of the rain gauge locations in a basin. INTRODUCTION We propose a simple procedure for the real-time estimation of the average rainfall over a catchment area from rainfall measurements made at a few measurement stations in that area. The estimation of such areal rainfall is an important step in many hydrological applications, such as evaluation of hydraulic balances, management of surface water resources, or real-time forecasting of river flows. For this last application the rainfall over the river basin is, of course, the main input to any rainfall-river flow fo.recasting model [Lorent and Gevers, 1976]. Following previous contributions [Creutin and Obled, 1982; Rodri•iuez-Iturbe and Mefia, 1974; Chua and Bras, 1982], the rainfall over a basin is modeled as a two-dimensional random

The adsorption characteristics of polyacrylamide polymer on iron ore tailings have been studied to understand the mechanism of adsorption. Adsorptions of both the anionic and non-ionic flocculants were analyzed using Langmuir isotherm and Freundlich isotherm. It was found that in comparison to the Langmuir model the Freundlich model was a better fit to the adsorption data according to the minimum variance criterion. It was established with the support of the Langmuir model that the adsorption of anionic and non-ionic flocculants is facilitated by hydrogen bonding. The zeta potential affects the settling rate and in this case the isoelectric point of the tailings which is basically a mixture of various oxides was measured to be 4.66. The settling rate was found to increase when the pH decreased from 10 to 5. The settling rate increased with increasing flocculant dosage up to a maximum value at 80 g polymer/t solid corresponding to the maximum adsorption of polymer. However, at higher pH the clarity of supernatant liquid was very poor and flocculation was not effective for ultrafine particles at that pH. with the tailings. The particle sizes of tailings are ultrafine in nature ranging from 1 to 45 m with a d 50 of around 7 m. It is important to mention that the iron ore tailings contain heterogeneous mixtures of iron oxides, silicates and aluminium-silicates. These tailings contain 40-50% (w/w) iron. The solid percentage in the tailings varies from 5 to 10% (w/w). The pH of the water in the tailings varies from 5.5 to 6.5. The beneficiation process requires the makeup water at around of 300-500 l/t of ore processed. It is essential to maximize the water recovery from the products and tailings by using dewatering techniques. Polymeric flocculation finds a wide application for dewatering in industries especially involving mineral processing, hydrometallurgy, and water treatment [1-3]. These polymers may be anionic, cationic or non-ionic. In flocculation, fine particulates suspended in liquid, interact with the flocculating agent and consequently aggregate to form flocs which settle rapidly under the influence of gravity. The flocculation process primarily involves transport of a particle to the closest distance of approach of another particle leading to collision and adhesion of particles resulting in aggregation and formation of flocs . The characteristics of flocs depend upon several factors such as surface chemistry, particle size distribution, density and shape of particle, viscosity and dielectric constant of suspension, chemical nature, molecular weight, charge and charge density of flocculant . It has been observed that polymers can flocculate ultrafine particles through various mechanisms such as bridging, charge neutralization, electrostatic patch and depletion flocculation . Ray and Hogg reported that bridging occurs by addition of high molecular weight polymer which forms the link 1385-8947/$ -see front matter

In this paper some distributional properties of the generalized order statistics from two parameter exponential distribution are given. The minimum variance linear unbiased estimators of the parameters and an important characterization of the exponential distribution are presented.

210 Pb and 137 Cs dating methods, accompanied by a high-resolution geochemical study, were applied to intertidal sediments containing both fine and coarse-grained particles and also, anthropogenic Pb in order to establish sedimentation rates and historical trends in heavy metal input. Sedimentation rates were established according to the ''Constant Flux:Constant Sedimentation'' (CF:CS) 210 Pb dating model, which was preferred rather than the ''Constant Rate of Supply-Minimum Variance'' (CRS-MV) model. Variations in sediment grain-size were accounted for by application of several normalization procedures. Al was selected for grain-size correction. Corrected sedimentation rates obtained from 210 Pb dating were corroborated through a second independent radionuclide tracer and by comparison of peak trace metal inputs into the environment with peaks in the sediment. The Chernobyl maximum was identified in the normalized 137 Cs activity profile. Sedimentation rates of 6.2 AE 1.2 mm y À1 and 3.1 AE 0.5 mm y À1 for the upper (two muddy layers) and 6.0 AE 2.0 mm y À1 for the lower (sandy) intertidal mud flat deposits of San Simón Bay were determined. According to the established chronology, human-induced environmental changes were detected in total metal concentrations (Cu, Pb, Zn) and in sediment grain-size and composition.

Region growing is a very useful technique for image segmentation. Its efficiency mainly depends on its aggregation criterion. In the present paper, a new algorithm is proposed with a homogeneity criterion based on an adequate tuning between spatial neighbourhood and histogram neighbourhood. It differs from other techniques by reconsidering the pixel (or voxel) assignments on each step by a process which minimizes variance through special dilations. Thus, the region created by an initial seed can be non-connected and possibly does not contain this seed. Examples are given in dental surgery for 2D X-Ray images (and their associated 3D block) and for 3D images acquired by the Morphometre, the new 3D scanner constructed by GEMSE (General Electric Medical Systems). © 1997 Published by Elsevier Science B.V.

Mean-variance portfolios constructed using the sample mean and covariance matrix of asset returns perform poorly out-of-sample due to estimation error. Moreover, it is commonly accepted that estimation error in the sample mean is much larger than in the sample covariance matrix. For this reason, practitioners and researchers have recently focused on the minimum-variance portfolio, which relies solely on estimates of the covariance matrix, and thus, usually performs better out-of-sample. But even the minimum-variance portfolios are quite sensitive to estimation error and have unstable weights that fluctuate substantially over time. In this paper, we propose a class of portfolios that have better stability properties than the traditional minimum-variance portfolios. The proposed portfolios are constructed using certain robust estimators and can be computed by solving a single nonlinear program, where robust estimation and portfolio optimization are performed in a single step. We show analytically that the resulting portfolio weights are less sensitive to changes in the asset-return distribution than those of the traditional minimum-variance portfolios. Moreover, our numerical results on simulated and empirical data confirm that the proposed portfolios are more stable than the traditional minimum-variance portfolios, while preserving (or slightly improving) their relatively good out-of-sample performance.

With institutional investors increasingly involved in alternative investments, portfolio optimisation within a large universe of hedge funds has become a key area for research. This paper develops a portfolio construction model that is specifically designed for funds of hedge funds, incorporating specific controls for operational limitations, data biases and incompleteness.

This paper investigates the effects of the long-run relationship between stock cash index and futures index on the hedging effectiveness of six stock futures markets. Effectiveness of five different hedging ratios depending on different estimation procedures is investigated. The unhedged, the traditional hedge and the minimum variance hedge ratios are all constant while the bivariate GARCH and GARCH-X hedge ratios are time varying. The effectiveness of the hedge ratio is compared by investigating the total sample and the out-of-sample performance of the five ratios. The total sample period consists of daily returns from (1 year). Results show that the time-varying hedge ratio outperforms the constant hedge ratio. #

We applied a new method of imaging frequency-specific changes in brain activity in humans during a finger brushing task in order to measure changes in cortical rhythms during tactile stimulation. Neuromagnetic recordings were conducted in five subjects using a whole-head MEG system during tactile stimulation of the right index finger, with or without visual feedback, and while viewing another individual's index finger being stimulated. Volumetric images of changes in source power relative to pre-stimulus baseline levels were computed with 2 mm resolution over the entire brain using a minimum-variance beamforming algorithm (synthetic aperture magnetometry). Onset of tactile stimulation produced a brief (200-300 ms) suppression of mu band (8-15 Hz) and beta band (15-30 Hz) cortical activity in the primary somatosensory and primary motor cortex, respectively, followed by a bilateral increase in beta band activity ('beta rebound') in motor cortex. This pattern of suppression...

A price process is scale-invariant if and only if the returns distribution is independent of the price level. We show that scale invariance preserves the homogeneity of a pay-off function throughout the life of the claim and hence prove that standard price hedge ratios for a wide class of contingent claims are model-free. Since options on traded assets are normally priced using some form of scale-invariant process, e.g. a stochastic volatility, jump diffusion or Lévy process, this result has important implications for the hedging literature.

Ahtract-This paper is concerned with the problem of estimating the state of a linear dynamic system using noise-corrupted observations, when input disturbances and observation errors are onknown except for the fact that they belong to given bounded sets. The cases of both energy constraints and individual instantaneous constraints for the uncertain quantities are considered. In the former case, the set of possible system states compatible with the observations received is shown to be an ellipsoid, and equations for its center and weighting matrix are given, while in the latter case, equations describing a boonding ellipsoid to the set of possible states are derived. All three problems of filtering, prediction, and smoothing are examined by relating them to standard tracking problems of optimal control theory. The resulting estimators are similar in strnctnre and comparable in simplicity to the corresponding stochastic linear minimum-variance estimators, and it is shown that they provide distinct advantages over existing schemes for recursive estimation with a set-membership description of uncertainty.

A price process is scale-invariant if and only if the returns distribution is independent of the price measurement scale. We show that most stochastic processes used for pricing options on financial assets have this property and that many models not previously recognised as scale-invariant are indeed so. We also prove that price hedge ratios for a wide class of contingent claims under a wide class of pricing models are model-free. In particular, previous results on model-free price hedge ratios of vanilla options based on scale-invariant models are extended to any contingent claim with homogeneous pay-off, including complex, path-dependent options. However, model-free hedge ratios only have the minimum variance property in scale-invariant stochastic volatility models when price-volatility correlation is zero. In other stochastic volatility models and in scale-invariant local volatility models, model-free hedge ratios are not minimum variance ratios and our empirical results demonstrate that they are less efficient than minimum variance hedge ratios.

... 27-51, 1970. 23. Jagannathan, R. and Ma, T., "Risk reduction in large portfolios: Why imposing the wrong constraints helps," J. Finance, v58, pp. 1651-1684, 2003. ... Lorenzo Garlappi: colleagues. Francisco J. Nogales: colleagues. Raman Uppal: colleagues. ...

In this paper we consider the weights of the global minimum variance portfolio (GMVP). The returns are assumed to follow a matrix elliptically contoured distribution, i.e., the returns are assumed to be neither independent nor normally distributed. A test for the general linear hypothesis is given. The distribution of the test statistic is derived under the null and the alternative hypothesis. It turns out that its distribution is invariant with respect to the type of the matrix elliptical distribution, i.e., the stochastic properties of the GMVP do not depend either on the mean vector or on the distributional assumptions imposed on asset returns. In an empirical study we analyze an international diversified portfolio.

This paper deals with the problem of microphone array speech enhancement using a hybrid Generalized Sidelobe Canceller (GSC) and Super-Directive Beamformer (SDB). While GSC is one of the most practical architectures for reducing the directional noises, SDB is a superior choice in the case of diffuse noise fields. In this research, we have combined these two structures to improve the performance of speech enhancement system in realistic noisy conditions. Furthermore, we have employed a Linear Constrained Minimum Variance (LCMV) beamformer instead of blocking matrix (in GSC) to generalize the good performance of the system for different arrival directions of desired speech. Finally, we have proposed nested sub-array implementation of the hybrid system to take advantages of the subband processing of wideband speech signal. Our experiments show the effectiveness of the proposed modifications in different input SNR values. The comparative evaluations demonstrate the superiority of the proposed system in noise reduction from speech in real-life conditions (where diffuse, incoherent, and directional noises are present, simultaneously).

This work investigated the potential of shea butter oil (SBO) as feedstock for synthesis of biodiesel. Due to high free fatty acid (FFA) of SBO used, response surface methodology (RSM) was employed to model and optimize the pretreatment step while its conversion to biodiesel was modeled and optimized using RSM and artificial neural network (ANN). The acid value of the SBO was reduced to 1.19 mg KOH/g with oil/ methanol molar ratio of 3.3, H 2 SO 4 of 0.15 v/v, time of 60 min and temperature of 45 C. Optimum values predicted for the transesterification reaction by RSM were temperature of 90 C, KOH of 0.6 w/v, oil/ methanol molar ratio of 3.5, and time of 30 min with actual shea butter oil biodiesel (SBOB) yield of 99.65% (w/w). ANN combined with generic algorithm gave the optimal condition as temperature of 82 C, KOH of 0.40 w/v, oil/methanol molar ratio of 2.62 and time of 30 min with actual SBOB yield of 99.94% (w/w). Coefficient of determination (R 2 ) and absolute average deviation (AAD) of the models were 0.9923, 0.83% (RSM) and 0.9991, 0.15% (ANN), which demonstrated that ANN model was more efficient than RSM model. Properties of SBOB produced were within biodiesel standard specifications.

Stratified sampling is a methodology in which a heterogeneous population is partitioned into homogeneous subgroups called strata. The focus is on solving the combined problem of sample allocation and stratum boundary determination with the genetic algorithm (GA). Assuming that the number of strata and the total sample size are arbitrarily predetermined, stratum boundaries are determined using an objective function of minimum variance of the estimator; with sample size allocated through equal, proportional, Neyman, and GA allocation methods. Some numerical examples are given and the performance of GA is compared with the geometric and the cumulative root frequency methods.

This paper considers the problem of unsupervised spectral unmixing for hyperspectral image analysis. Each observed pixel is assumed to be a noisy linear mixture of pure material spectra, namely, endmembers. The mixing coefficients, usually called abundances, are constrained to positive and summed to unity. The proposed unmixing approach is based on the nonnegative matrix factorization (NMF) framework, which considers the physical constraints of the problem, including the positivity of the endmember spectra and abundances. However, the basic NMF formulation has degenerated solutions and suffers from nonconvexity limitations. We consider here a regularization function, called dispersion, which favors the solution such that the endmember spectra have minimum variances. Such a solution encourages the recovered spectra to be flat, preserving the possible spectral singularities (peaks and sharp variations). The regularized criterion is minimized with a projected gradient (PG) scheme, and we propose a new step-size estimation technique to fasten the PG convergence. The derived algorithm is called MiniDisCo, for minimum dispersion constrained NMF. We experimentally compare MiniDisCo with the recently proposed algorithm. It is shown to be particularly robust to the presence of flat spectra, to a possible a priori overestimation of the number of endmembers, or if the amount of observed spectral pixels is low. In addition, experiments show that the considered regularization correctly overcomes the degeneracy and nonconvexity problems, leading to satisfactory unmixing accuracy. We include a comparative analysis of a real-world scene.

A b s t r a c t. An evaluation of the efficiency of different methods of the minimum variance portfolio selection was performed for seventy stocks from the Warsaw Stock Exchange. Eight specifications of multivariate GARCH models and six other methods were used. The application of all considered GARCH-class models was more efficient in stocks allocation than the implementation of the other analyzed methods. The simple specifications of multivariate GARCH models, whose parameters were estimated in two stages, like the DCC and CCC models were the best performing models. K e y w o r d s: multivariate GARCH models, time-varying covariance matrix, portfolio selection.

In this paper, we extend the mean-variance portfolio model where expected returns are obtained using maximum likelihood estimation to explicitly account for uncertainty about the estimated expected returns. In contrast to the Bayesian approach to estimation error, where there is only a single prior and the investor is neutral to uncertainty, we allow for multiple priors and aversion to uncertainty. We characterize the set of priors as a confidence interval around the estimated value of expected return and we model aversion to uncertainty via a minimization over the set of priors. The multi-prior model has several attractive features: One, just like the Bayesian model, the multi-prior model is firmly grounded in decision theory; Two, it is flexible enough to allow for uncertainty about expected returns estimated jointly for all assets or different levels of uncertainty about expected returns for different subsets of the assets; Three, we show how in several special cases of the multi-prior model one can obtain closed-form expressions for the optimal portfolio, which can be interpreted as a shrinkage of the mean-variance portfolio towards either the risk-free asset or the minimum variance portfolio. We illustrate how to implement the multi-prior model using both international and domestic data. Our analysis suggests that allowing for parameter uncertainty reduces the fluctuation of portfolio weights over time and, for the data set considered, improves the out-of sample performance.

In applications such as fishery sonar and navigation, cylindrical or spherical arrays are often used because of the need for a 360 field of view. However, adaptive beamforming methods, known for their high angular resolution and interference rejection capabilities, often rely on a Vandermonde structure of the steering vectors. This is generally not the case for nonlinear arrays. In this paper, we use an interpolated array transformation to map the data to a virtual linear array before adaptive beamforming. We evaluate the performance of two different adaptive beamformers using simulations as well as experimental data from the SX90 fish finding sonar. We show that the adaptive minimum variance (MV) and amplitude and phase estimation of a sinusoid (APES) beamformers offer a significant improvement in azimuth resolution compared to the conventional delay-and-sum (DAS) beamformer. The APES beamformer offers slightly more reliable amplitude estimates in the direction of interest compared to the MV beamformer, at the cost of a somewhat lower azimuth resolution. When applied to data from the SX90 fish finding sonar, the MV beamformer offers a 40%-50% improvement in resolution, while the APES beamformer offers an improvement of 20%-30%.

The Kalman filter is the minimum-variance state estimator for linear dynamic systems with Gaussian noise. Even if the noise is non-Gaussian, the Kalman filter is the best linear estimator. For nonlinear systems it is not possible, in general, to derive the optimal state estimator in closed form, but various modifications of the Kalman filter can be used to estimate the state. These modifications include the extended Kalman filter, the unscented Kalman filter, and the particle filter. Although the Kalman filter and its modifications are powerful tools for state estimation, we might have information about a system that the Kalman filter does not incorporate. For example, we may know that the states satisfy equality or inequality constraints. In this case we can modify the Kalman filter to exploit this additional information and get better filtering performance than the Kalman filter provides. This paper provides an overview of various ways to incorporate state constraints in the Kalman filter and its nonlinear modifications. If both the system and state constraints are linear, then all of these different approaches result in the same state estimate, which is the optimal constrained linear state estimate. If either the system or constraints are nonlinear, then constrained filtering is, in general, not optimal, and different approaches give different results.

Models of human movement from computational neuroscience provide a starting point for building a system that can produce flexible adaptive movement on a robot. There have been many computational models of human upper limb movement put forward, each attempting to explain one or more of the stereotypical features that characterize such movements. While these models successfully capture some of the features of human movement, they often lack a compelling biological basis for the criteria they choose to optimize. One that does provide such a basis is the minimum variance model (and its extension—task optimization in the presence of signal-dependent noise). Here, the variance of the hand position at the end of a movement is minimized, given that the control signals on the arm's actuators are subject to random noise with zero mean and variance proportional to the amplitude of the signal. Since large control signals, required to move fast, would have higher amplitude noise, the speed-accuracy trade-off emerges as a direct result of the optimization process. We chose to implement a version of this model that would be suitable for the control of a robot arm, using an optimal control scheme based on the discrete-time linear quadratic regulator. This implementation allowed us to examine the applicability of the minimum variance model to producing humanlike movement. In this paper, we describe our implementation of the minimum variance model, both for point-to-point reaching movements and for more complex trajectories involving via points. We also evaluate its performance in producing humanlike movement and show its advantages over other optimization based models (the well-known minimum jerk and minimum torque-change models) for the control of a robot arm. © 2005 Wiley Periodicals, Inc.

Deep brain stimulation (DBS) is an effective therapy to treat movement disorders including essential tremor, dystonia, and Parkinson's disease. Despite over a decade of clinical experience the mechanisms of DBS are still unclear, and this lack of understanding makes the selection of stimulation parameters quite challenging. The objective of this work was to develop a closed-loop control system that automatically adjusted the stimulation amplitude to reduce oscillatory neuronal activity, based on feedback of electrical signals recorded from the brain using the same electrode as implanted for stimulation. We simulated a population of 100 intrinsically active model neurons in the Vim thalamus, and the local field potentials (LFPs) generated by the population were used as the feedback (control) variable for closed loop control of DBS amplitude. Based on the correlation between the spectral content of the thalamic activity and tremor (Hua et al., 1998), (Lenz et al., 1988), we implemented an adaptive minimum variance controller to regulate the power spectrum of the simulated LFPs and restore the LFP power spectrum present under tremor conditions to a reference profile derived under tremor free conditions. The controller was based on a recursively identified autoregressive model (ARX) of the relationship between stimulation input and LFP output, and showed excellent performances in tracking the reference spectral features through selective changes in the theta (2-7 Hz), alpha (7-13 Hz), and beta (13-35 Hz) frequency ranges. Such changes reflected modifications in the firing patterns of the model neuronal population, and, differently from open-loop DBS, replaced the tremor-related pathological patterns with patterns similar to those simulated in tremor-free conditions. The closed-loop controller generated a LFP spectrum that approximated more closely the spectrum present in the tremor-free condition than did open loop fixed intensity stimulation and adapted to match the spectrum after a change in the neuronal oscillation frequency. This computational study suggests the feasibility of closed-loop control of DBS amplitude to regulate the spectrum of the local field potentials and thereby normalize the aberrant pattern of neuronal activity present in tremor.

This paper provides a tutorial introduction to the role of the time-delay or the interactor matrix in multivariate minimum variance control. Minimum variance control gives the lowest achievable output variance and thus serves as a useful benchmark for performance assessment. One of the major drawbacks of the multivariate minimum variance benchmark is the need for apriori knowledge of the multivariate time-delay matrix. A graphical method of multivariate performance assessment known as the Normalized Multivariate Impulse Response (NMIR), that does not require knowledge of the interactor, is proposed in this paper. The use of NMIR as a performance assessment tool is illustrated by application to two multivariate controllers. Two additional performance benchmarks are introduced as alternatives to the minimum variance benchmark, and their application is illustrated by a simulated example. A detailed performance evaluation of an industrial MPC controller is presented. The diagnosis steps in identifying the cause of poor performance, e.g. as due to model-plant mismatch, are illustrated on the same industrial case study.

Pedotransfer functions (PTFs) have become a ‘white-hot’ topic in the area of soil science and environmental research. Most current PTF research focuses only on the development of new functions for predicting soil physical and chemical properties for different geographical areas or soil types while there are also efforts to collate and use the available PTFs. This paper reviews the brief history of the use of pedotransfer functions and discusses types of PTFs that exist. Different approaches to developing PTFs are considered and we suggest some principles for developing and using PTFs.We propose the concept of the soil inference systems (SINFERS), where pedotransfer functions are the knowledge rules for inference engines. A soil inference system takes measurements we more-or-less know with a given level of (un)certainty, and infers data that we do not know with minimal inaccuracy, by means of properly and logically conjoined pedotransfer functions. The soil inference system has a source, an organiser and a predictor. The sources of knowledge to predict soil properties are collections of pedotransfer functions and soil databases. The organiser arranges and categorises the PTFs with respect to their required inputs and the soil types from which they were generated. The inference engine is a collection of logical rules selecting the PTFs with the minimum variance. Uncertainty of the prediction can be assessed using Monte Carlo simulations. The inference system will return the predictions of soil physical and chemical properties with their uncertainties based on the information provided. Uncertainty in the prediction can be quantified in terms of the model uncertainty and input data uncertainty. In order to avoid extrapolation, a method was developed to quantify the degree of belonging of a soil sample within the training set of a PTF.With the first approach to a soil inference system, we can optimally predict various important physical and chemical properties from the information we have utilising PTFs as the knowledge rules.

Iverson, claimed that statistic p rep overestimates the "true probability of replication. " We show that Iverson et al. confused the probability of replication of an observed direction of effect with a probability of coincidence-the probability that two future experiments will return the same sign. The theoretical analysis is punctuated with a simulation of the predictions of p rep for a realistic random effects world of representative parameters, when those are unknown a priori. We emphasize throughout that p rep is intended to evaluate the probability of a replication outcome after observations, not to estimate a parameter. Hence, the usual conventional criteria (unbiasedness, minimum variance estimator) for judging estimators are not appropriate for probabilities such as p and p rep .

The existing linear algorithms exhibit various high sensitivities to noise. The analysis presented in this paper provides insight into the causes for such high sensitivities. It is shown in this paper that even a small pixel-level perturbation may override the epipolar information that is essential for the linear algorithms to distinguish different motions. This analysis indicates the need for optimal estimation in the presence of noise. Then, we introduce methods for optimal motion and structure estimation under two situations of noise distribution: 1) known and 2) unknown. Computationally, the optimal estimation amounts to minimizing a nonlinear function. For the correct convergence of this nonlinear minimization, we use a two-step approach. The first step is using a linear algorithm to give a preliminary estimate for the parameters. The second step is minimizing the optimal objective function starting from that preliminary estimate as an initial guess. A remarkable accuracy improvement has been achieved by this two-step approach over using the linear algorithm alone. In order to assess the accuracy of the optimal solution, the error in the solution of the optimal estimation algorithm is compared with a theoretical lower error bound-CramCr-Rao bound. The simulations have shown that with Gaussian noise added to the coordinates of the image points, the actual error in the optimal solution is very close to the bound. In addition, we also use the CramCr-Rao bound to indicate the inherent instability of motion estimation from small image disparities, such as motion from optical flow. Finally, it is known that given the same nonlinear objective function and the same initial guess, different minimization methods may lead to different solutions. We investigate the performance difference between a batch least-squares technique (Levenberg-Marquardt) and a sequential least-squares technique (iterated extended Kalman filter) for this motion estimation problem, and the simulations showed that the former gives better results.

A radar system composed of a single transmitter, M receiving channels is studied. Radar echo signals are acquired to estimate the angle, range and velocity in a multiple moving target scenario. The developed algorithm is based on sparse recovery technique by exploiting the sparseness of the targets in anglerange domain. It is shown in simulations for automotive scenario that the proposed algorithm yield better performance in terms of both imaging accuracy and multiple-target resolution compared with the methods of conventional beamforming and minimum variance (Capon) beamforming.

This paper presents an efficient adaptive combination strategy for the distributed estimation problem over diffusion networks in order to improve robustness against the spatial variation of signal and noise statistics over the network. The concept of minimum variance unbiased estimation is used to derive the proposed adaptive combiner in a systematic way. The mean, mean-square, and steady-state performance analyses of the diffusion least-mean squares (LMS) algorithms with adaptive combiners are included and the stability of convex combination rules is proved. Simulation results show i) that the diffusion LMS algorithm with the proposed adaptive combiners outperforms those with existing static combiners and the incremental LMS algorithm, and ii) that the theoretical analysis provides a good approximation of practical performance.

Variance-based thresholding methods could be biased from the threshold found by expert and the underlying mechanism responsible for this bias is explored in this paper. An analysis on the minimum class variance thresholding (MCVT) and the Otsu method, which minimizes the within-class variance, is carried out. It turns out that the bias for the Otsu method is due to differences in class variances or class probabilities and the resulting threshold is biased towards the component with larger class variance or larger class probability. The MCVT method is found to be similar to the minimum error thresholding.

Optimal or unbiased estimators are widely used for state estimation and tracking. We propose a new minimum variance unbiased (MVU)finite impulse response (FIR)filter which minimizes the estimation error variance in the unbiased FIR (UFIR)filter. The relationship between thefilter gains of the MVU FIR, UFIR and optimal FIR (OFIR)filters is found analytically. Simulations provided using a polynomial state-space model have shown that errors in the MVU FIRfilter are intermediate between the UFIR and OFIR filters, and the MVU FIR filter exhibits better denoising effect than the UFIR estimates. It is also shown that the performance of MVU FIR filter strongly depends on the averaging interval of N points: by small N,theMVUFIRfilter approaches UFIR filter and, ifN is large, it becomes optimal.

We examine the use of second-order stochastic dominance as both a technique for constructing portfolios and also as a way to measure performance. As a preference-free technique second-order stochastic dominance will suit any risk-averse investor, and it does not require normally distributed returns. Using in-sample data, we construct portfolios such that their second-order stochastic dominance over a benchmark is most probable. The empirical results based on 21 years of daily data suggest that this portfolio choice technique significantly outperforms the benchmark out-of-sample. Moreover, its performance is typically better -and frequently much better -than several alternative portfolio-choice approaches using equal weights, mean-variance optimization, or minimum-variance methods.

In this paper some distributional properties of the generalized order statistics from two parameter exponential distribution are given. The minimum variance linear unbiased estimators of the parameters and an important characterization of the exponential distribution are presented.

Purpose -The purpose of this paper is to provide a clustering approach to segment supply chain partners in the automobile industry and prioritize services offered by third party logistics service (3PL) providers. Design/methodology/approach -In total, 98 automobile and auto-parts manufacturers are surveyed to identify service needs, preferences, and outsourcing commitments. By applying a two-stage clustering approach combined with Ward's minimum-variance method and the K-means algorithm, the logistics companies prioritize their services to better satisfy groups of customers with specific preferences. Findings -Four distinctive groups of manufacturers are identified using the two-stage clustering approach. The clusters separate logistic preferences and outsourcing patterns of after market parts suppliers, original equipment service parts suppliers, original equipment manufacturer parts suppliers, and tier one car makers. The paper finds that distribution and delivery services hold the highest percentage of services outsourced among the manufacturers. Originality/value -This paper models logistic services as customizable services and develops a data system methodology to define the profiles of automobile manufacturers and their preferred logistic services. Through the analysis of service preferences and clustering, the paper identifies the key logistic services that can be customized for members of the automobile supply chain. A case is provided which demonstrates how a logistics company can provide customized service designs for specific target markets and customers.

Photoacoustic signals, detected by a transducer array, need to be beamformed for subsequent use in a limited view angle tomography such as B-scan imaging. In the presence of the light scattering or phase aberration, the spatial resolution and contrast in the photoacoustic images are degraded. Phase aberration due to tissues with inhomogeneous acoustic speeds is a major source for image degradation. However, a constant speed of sound (e.g., 1540 m/s) is typically assumed in photoacoustic imaging. Such an assumption can affect the quality of photoacoustic image since changes in sound velocity cause significant phase errors in beamforming. An adaptive weighting method such as coherence factor (CF) technique can improve the ultrasound and photoacoustic image quality significantly. In addition, photoacoustic images can be further improved by applying adaptive beamforming techniques developed for ultrasound imaging. In this study, an adaptive photoacoustic image reconstruction technique that combines an adaptive weighting factor (CF) and an adaptive apodization called minimum variance method (MV) is introduced. Although MV method calculates the optimal apodization weighting factors which minimize the variance of the beamformed signal, it can lead to unexpected weighting factors since it is data dependant. In this case, CF weighting can help to avoid this problem by weighting the output from the MV method based on signal coherence. Simulations were performed to analyze the spatial resolution using a point targets and to demonstrate improvement in phase aberration correction. Numerical studies demonstrated the superior performance of MV adaptive method combined with CF weighting.

Minimum-variance unbiased linear estimation theory has found many applications in the analysis of spatial rainfall and hydrogeologic data: estimation of point values or areal averages, calculation of variances of estimation error, and network design. However, the important problem of inferring the spatial structure or interdependence of the function of interest has received relatively less attention. Three methods for the estimation of the parameters of Matheron's polynomial generalized covariance function (a useful model for nonstationary functions) are presented and evaluated: Maximum likelihood (ML), minimum variance unbiased quadratic (MVUQ), and minimum norm (least squares). The estimation error covariance matrix of the parameters is calculated with each of these methods. ML and MVUQ estimation have very good properties and, for reasonably large samples, give very similar results. Minimum norm estimation is appropriate for preliminary data analysis. The application of these methodologies is illustrated with a set of rainfall data, and problems of implementation are discussed. It is shown that the estimation of the parameters of the covariance function involves sizeable errors. It is suggested that, in practice, it may be rather difficult to identify the parameters of all but simple models. It is important that future research evaluate the effects of parameter uncertainty in the circulation of estimation error variances of point or areal averages and in the design of hydrologic data collection networks.

Ultrasonic guided wave imaging with a sparse, or spatially distributed, array can detect and localize damage over large areas. Conventional delay-and-sum images from such an array typically have a relatively high noise floor, however, and contain artifacts that often cannot be discriminated from damage. Considered here is minimum variance distortionless response (MVDR) imaging, which is a variation of delay-and-sum imaging whereby weighting coefficients are adaptively computed at each pixel location. Utilization of MVDR significantly improves image quality compared with delay-and-sum imaging, and additional improvements are obtained from incorporation of a priori scattering information in the MVDR method, use of phase information, and instantaneous windowing. Simulated data from a through-hole scatterer are used to illustrate performance improvements, and a performance metric is proposed that allows for quantitative comparisons of images from a known scatterer. Experimental results from a through-hole scatterer are also provided that illustrate imaging efficacy.