Sequential estimation

We present in this paper optimal and accelerated row projection algorithms arising from the use of quadratic programming, that allow us to define the iterate x k+1 as the projection of x k onto a hyperplane which minimizes its distance to the solution x * . These algorithms also use a novel partition strategy into blocks based on sequential estimations of their condition numbers.

A parameter estimation problem is considered, in which dispersed sensors transmit to the statistician partial information regarding their observations. The sensors observe the paths of continuous semimartingales, whose drifts are linear with respect to a common parameter. A novel estimating scheme is suggested, according to which each sensor transmits only one-bit messages at stopping times of its local filtration. The proposed estimator is shown to be consistent and, for a large class of processes, asymptotically optimal, in the sense that its asymptotic distribution is the same as the exact distribution of the optimal estimator that has full access to the sensor observations. These properties are established under an asymptotically low rate of communication between the sensors and the statistician. Thus, despite being asymptotically efficient, the proposed estimator requires minimal transmission activity, which is a desirable property in many applications. Finally, the case of discrete sampling at the sensors is studied when their underlying processes are independent Brownian motions.

This paper presents a new method for tracking a mobile based on Aulin's wave scattering model. This model takes into account non line of sight and multipath propagation environments, which are usually encountered in wireless fading channels. According to Aulin's model, the received instantaneous electric field at the base station is a nonlinear function of the mobile location and velocity. A method based on particle filtering (sequential Monte Carlo methods) that copes with nonlinearities in order to estimate the mobile location and velocity is proposed. In contrast to standard target tracking literature we do not rely on linearized motion models, measurement relations, and Gaussian assumptions. Numerical results are presented to evaluate the accuracy of the proposed method. They demonstrate significant accuracy improvement over known algorithms.

We consider linear dynamical systems, particularly coupled linear oscillators, where the parameters represent meaningful values in a domain theory, and thus learning what affects them contributes to explanation. Rather than allow perturbations of latent states, we assume that temporal variation beyond noise is explained by parameter drift, and variation across coupled systems is a function of moderating variables. This change in model structure reduces opportunities for efficient inference, and we propose sampling procedures to learn and fit the models. We test our approach on a real dataset of self-recalled emotional experience measurements of heterosexual couples engaged in a conversation about a potentially emotional topic, with body mass index (BMI) being considered as a moderator. We evaluate several models on their ability to predict future conversation dynamics (the last 20% of the data for each test couple), with shared parameters being learned using held out data. We valida...

Recent, advances in blind channel equalization approiiches and the availabil ity of fast processors have made it, possilile to communicate reliably over long distances through HF communication links. Current research efforts focus on the improvement of the performance of the communication systems which de grades significantly during the "bad tropospheric conditions" when the channel characteristics show rapid variations. In order to improve the performance of the HF communication links during these conditions, algorithms that can identify and track the channel charac teristics are proposed in this thesis. Detailed simulation based comparisons with the existing algorithms show that the proposed approaches significantly improve the performance of the communication system and enable us to utilize HF communication in bad conditions even at 10 dB SNR.

The problem of inferring 3D orientation of a camera from video sequences has been mostly addressed by first computing correspondences of image features. This intermediate step is now seen as the main bottleneck of those approaches. In this paper, we propose a new 3D orientation estimation method for urban (indoor and outdoor) environments, which avoids correspondences between frames. The scene property exploited by our method is that many edges are oriented along three orthogonal directions; this is the recently introduced Manhattan world (MW) assumption. The main contributions of this paper are: the definition of equivalence classes of equiprojective orientations, the introduction of a new small rotation model, formalizing the fact that the camera moves smoothly, and the decoupling of elevation and twist angle estimation from that of the compass angle. We build a probabilistic sequential orientation estimation method, based on an MW likelihood model, with the above-listed contributions allowing a drastic reduction of the search space for each orientation estimate. We demonstrate the performance of our method using real video sequences.

Kalman filtering techniques are combined with a semianalytical orbit generator to develop a sequential orbit determination algorithm. The algorithm is investigated for computational efficiency, accuracy, and radius of convergence by comparison with truth ...

In this paper, we detail the hardware and software perception system designed and developed to track pedestrians using a set of offboard cameras. It has been used in the context of vulnerable safety in a car park. This architecture is divided in two parts: a fusion part to fusion the data given by the set of offboard cameras and a tracking part to sequentially estimate the position of each pedestrian present in the environment and to determine the number of pedestrians. Finally, some experimental results are presented.

We present in this paper optimal and accelerated row projection algorithms arising from the use of quadratic programming, that allow us to define the iterate x k+1 as the projection of x k onto a hyperplane which minimizes its distance to the solution x *. These algorithms also use a novel partition strategy into blocks based on sequential estimations of their condition numbers.

In this paper we discuss the multistage sequential estimation of the variance of the Rayleigh distribution using the three-stage procedure that was presented by Hall (Ann. Stat. 9(6):1229–1238, 1981). Since the Rayleigh distribution variance is a linear function of the distribution scale parameter’s square, it suffices to estimate the Rayleigh distribution’s scale parameter’s square. We tackle two estimation problems: first, the minimum risk point estimation problem under a squared-error loss function plus linear sampling cost, and the second is a fixed-width confidence interval estimation, using a unified optimal stopping rule. Such an estimation cannot be performed using fixed-width classical procedures due to the non-existence of a fixed sample size that simultaneously achieves both estimation problems. We find all the asymptotic results that enhanced finding the three-stage regret as well as the three-stage fixed-width confidence interval for the desired parameter. The procedure...

This paper discusses the sequential estimation of the scale parameter of the Rayleigh distribution using the three-stage sequential sampling procedure proposed by Hall (Ann. Stat.1981, 9, 1229–1238). Both point and confidence interval estimation are considered via a unified optimal decision framework, which enables one to make the maximum use of the available data and, at the same time, reduces the number of sampling operations by using bulk samples. The asymptotic characteristics of the proposed sampling procedure are fully discussed for both point and confidence interval estimation. Since the results are asymptotic, Monte Carlo simulation studies are conducted to provide the feel of small, moderate, and large sample size performance in typical situations using the Microsoft Developer Studio software. The procedure enjoys several interesting asymptotic characteristics illustrated by the asymptotic results and supported by simulation.

This letter presents an improved result on the negative-binomial Monte Carlo technique analyzed in a previous paper 1 for the estimation of an unknown probability p. Specifically, the confidence level associated to a relative interval \p/fi2, Pl^i], with fii, ¡12 > 1, is proved to exceed its asymptotic value for a broader range of intervals than that given in the referred paper, and for any value of p. This extends the applicability of the estimator, relaxing the conditions that guarantee a given confidence level.

Sequential estimation of a probability p by means of inverse binomial sampling is considered. For μ 1 , μ 2 > 1 given, the accuracy of an estimatorp is measured by the confidence level P [p/μ 2 ≤p ≤ pμ 1 ]. The confidence levels c 0 that can be guaranteed for p unknown, that is, such that P [p/μ 2 ≤p ≤ pμ 1 ] ≥ c 0 for all p ∈ (0, 1), are investigated. It is shown that within the general class of randomized or nonrandomized estimators based on inverse binomial sampling, there is a maximum c 0 that can be guaranteed for arbitrary p. A non-randomized estimator is given that achieves this maximum guaranteed confidence under mild conditions on μ 1 , μ 2 .

Let X 1 , X 2 ,. .. be a discrete-time stochastic process with a distribution P θ , θ ∈ Θ, where Θ is an open subset of the real line. We consider the problem of testing a simple hypothesis H 0 : θ = θ 0 versus a composite alternative H 1 : θ > θ 0 , where θ 0 ∈ Θ is some fixed point. The main goal of this article is to characterize the structure of locally most powerful sequential tests in this problem. For any sequential test (ψ, φ) with a (randomized) stopping rule ψ and a (randomized) decision rule φ let α(ψ, φ) be the type I error probability,β 0 (ψ, φ) the derivative, at θ = θ 0 , of the power function, and N (ψ) an average sample number of the test (ψ, φ). Then we are concerned with the problem of maximizingβ 0 (ψ, φ) in the class of all sequential tests such that α(ψ, φ) ≤ α and N (ψ) ≤ N , where α ∈ [0, 1] and N ≥ 1 are some restrictions. It is supposed that N (ψ) is calculated under some fixed (not necessarily coinciding with one of P θ) distribution of the process X 1 , X 2. .. . The structure of optimal sequential tests is characterized.

On-line analysis of output data from discrete event stochastic simulation focuses almost entirely on estimation of means. Most "variance estimation" research in simulation refers to the estimation of the variance of the mean, to construct confidence intervals for mean values. There has been little research on the estimation of variance in simulation. We investigate three methods for point and interval estimates of variance and discuss an implementation of the best technique in an extended version of Akaroa2, a quantitative stochastic simulation controller.

Abstract: Stochastic simulation has become a well established paradigm used in performance evaluation of various complex dynamic systems. Most simulation output analysis is confined to the estimation of mean values. This is true for both finite horizon and steady state simulation. The estimation of quantiles provides a deeper insight into the simulated model. In this paper we describe a method for estimating time evolution of several quantiles within some time interval. It is based on independent replications and its ...

This paper deals with the H ∞ recursive estimation problem for general rectangular time-variant descriptor systems in discrete time. Riccati-equation based recursions for filtered and predicted estimates are developed based on a data fitting approach and game theory. In this approach, the nature determines a state sequence seeking to maximize the estimation cost, whereas the estimator tries to find an estimate that brings the estimation cost to a minimum. A solution exists for a specified γ-level if the resulting cost is positive. In order to present some computational alternatives to the H ∞ filters developed, they are rewritten in information form along with the respective array algorithms.

In this article we prove new central limit theorems (CLT) for several coupled particle filters (CPFs). CPFs are used for the sequential estimation of the difference of expectations w.r.t. filters which are in some sense close. Examples include the estimation of the filtering distribution associated to different parameters (finite difference estimation) and filters associated to partially observed discretized diffusion processes (PODDP) and the implementation of the multilevel Monte Carlo (MLMC) identity. We develop new theory for CPFs and based upon several results, we propose a new CPF which approximates the maximal coupling (MCPF) of a pair of predictor distributions. In the context of ML estimation associated to PODDP with discretization ∆ l we show that the MCPF and the approach in [19] have, under assumptions, an asymptotic variance that is upper-bounded by an expression that is (almost) O(∆ l), uniformly in time. The O(∆ l) rate preserves the so-called forward rate of the diffusion in some scenarios which is not the case for the CPF in [21].

Sequential estimation of a vector of linear regression coefficients is considered under both centralized and decentralized setups. In sequential estimation, the number of observations used for estimation is determined by the observed samples, hence is random, as opposed to fixed-sample-size estimation. Specifically, after receiving a new sample, if a target accuracy level is reached, we stop and estimate using the samples collected so far; otherwise we continue to receive another sample. It is known that finding an optimum sequential estimator, which minimizes the average sample number for a given target accuracy level, is an intractable problem with a general stopping rule that depends on the complete observation history. By properly restricting the search space to stopping rules that depend on a specific subset of the complete observation history, we derive the optimum sequential estimator in the centralized case via optimal stopping theory. However, finding the optimum stopping rule in this case requires numerical computations that quadratically scales with the number of parameters to be estimated. For the decentralized setup with stringent energy constraints, under an alternative problem formulation that is conditional on the observed regressors, we first derive a simple optimum scheme whose computational complexity is constant with respect to the number of parameters. Then, following this simple optimum scheme we propose a decentralized sequential estimator whose computational complexity and energy consumption scales linearly with the number of parameters. Specifically, in the proposed decentralized scheme a close-to-optimum average stopping time performance is achieved by infrequently transmitting a single pulse with very short duration.

We consider the problem of simultaneous detection and estimation under a sequential framework. In particular we are interested in sequential tests that distinguish between the null and the alternative hypothesis and every time the decision is in favor of the alternative they provide an estimate of a random parameter. As we demonstrate with our analysis treating the two subproblems separately with the corresponding optimal strategies does not result in the best possible performance. To enjoy optimality one needs to take into account the optimum estimator during the hypothesis testing phase.

We develop optimal centralized sequential estimators under different formulations of the problem. Decentralized sequential estimation is also considered for wireless sensor networks. We propose an asymptotically optimal decentralized scheme based on level-triggered sampling, a non-uniform sampling technique. Performance of the proposed scheme is analyzed.

This paper proposes a procedure for the estimation of discrete Markov decision models and studies its statistical and computational properties. Our Nested Pseudo-Likelihood method (NPL) is similar to Rust's Nested Fixed Point algorithm (NFXP), but the nesting of the two algorithms is swapped. First, we prove that on convergence NPL produces a root of the likelihood equations. Our procedure requires fewer policy iterations at the expense of more likelihood-climbing iterations. We focus on a class of in¯nite-horizon, partial likelihood problems for which NPL can deliver large computational gains. Second, based on this algorithm we de¯ne a class of consistent and asymptotically equivalent Sequential Policy Iteration (PI) estimators, which encompasses both Hotz-Miller's CCP estimator and the partial Maximum Likelihood estimator. This presents the researcher with a "menu" of sequential estimators re°ecting a trade-o® between¯nite-sample precision and computational cost. Using actual and simulated data we compare the relative performance of these estimators. In all our experiments the bene¯ts in terms of precision of using a 2-stage PI estimator instead of 1-stage (i.e., Hotz-Miller) are very signi¯cant. More interestingly, the bene¯ts of MLE relative to 2-stage PI are small.

In this paper, a blind sequence estimation algorithm based on interacting multiple model is introduced to estimate the channel and the transmitted sequence corrupted by ISI (intersymbol interference) and noise. The proposed algorithm avoids the exponential growth complexity caused by increasing channel memory length. The performance of the IMM (interacting multiple model) based equalizer is studied and compared with the well known algorithm like DDFSE (Delayed Decision-Feedback Sequence Estimation).

This paper proposes a procedure for the estimation of discrete Markov decision models and studies its statistical and computational properties. Our Nested Pseudo-Likelihood method (NPL) is similar to Rust's Nested Fixed Point algorithm (NFXP), but the nesting of the two algorithms is swapped. First, we prove that on convergence NPL produces a root of the likelihood equations. Our procedure requires fewer policy iterations at the expense of more likelihood-climbing iterations. We focus on a class of in¯nite-horizon, partial likelihood problems for which NPL can deliver large computational gains. Second, based on this algorithm we de¯ne a class of consistent and asymptotically equivalent Sequential Policy Iteration (PI) estimators, which encompasses both Hotz-Miller's CCP estimator and the partial Maximum Likelihood estimator. This presents the researcher with a "menu" of sequential estimators re°ecting a trade-o® between¯nite-sample precision and computational cost. Using actual and simulated data we compare the relative performance of these estimators. In all our experiments the bene¯ts in terms of precision of using a 2-stage PI estimator instead of 1-stage (i.e., Hotz-Miller) are very signi¯cant. More interestingly, the bene¯ts of MLE relative to 2-stage PI are small.

Sequential analysis of simulation output is generally accepted as the most efficient way for securing representativeness of samples of collected observations. In this scenario a simulation experiment is stopped when the relative precision of estimates, defined as the relative width of confidence intervals at an assumed confidence level, reaches the required level. This paper deals with the statistical correctness of the methods proposed for estimating confidence intervals for mean values in sequential steady-state stochastic simulation. We formulate basic rules that should be followed in proper experimental analysis of coverage of different steadystate interval estimators. Our main argument is that such analysis should be done sequentially. The numerical results of our preliminary coverage analysis of the method of Spectral Analysis (SA/HW) and Nonoverlapping Batch Means are presented, and compared with those obtained by traditional, non-sequential approaches.

This paper evaluates the properties of a joint and sequential estimation procedure for estimating the parameters of single and multiple threshold models. We initially proceed under the assumption that the number of regimes is known à a priori but subsequently relax this assumption via the introduction of a model selection based procedure that allows the estimation of both the unknown parameters and their number to be performed jointly. Theoretical properties of the resulting estimators are derived and their ÿnite sample properties investigated.

This paper evaluates the properties of a joint and sequential estimation procedure for estimating the parameters of single and multiple threshold models. We initially proceed under the assumption that the number of regimes is known à a priori but subsequently relax this assumption via the introduction of a model selection based procedure that allows the estimation of both the unknown parameters and their number to be performed jointly. Theoretical properties of the resulting estimators are derived and their ÿnite sample properties investigated.

This paper presents an analysis of known rules of combination as well as a new method of combining uncertain evidence. The author concentrates on examination of the rules with accordance to target threat models. The examination have been taken with usage of the predefined measuring scenarios applied to information sources.

While inverse parameter estimation techniques for determining key parameters affecting water flow and solute transport are becoming increasingly common in saturated and unsaturated zone studies, their application to practical problems, such as irrigation, have received relatively little attention. In this article, we used the Levenberg-Marquardt optimization algorithm in combination with the HYDRUS-2D numerical code to estimate soil hydraulic and solute transport parameters of several soil horizons below experimental furrows. Three experiments were carried out, each of the same duration but with different amounts of water and solutes resulting from 6, 10, and 14 cm water depths in the furrows. Two more experiments were performed with the same amounts of applied water and solute and, consequently, for different durations, on furrows with depths of 6 and 10 cm of water. We first used a scaling method to characterize spatial variability in the soil hydraulic properties, and then simultaneously estimated the saturated hydraulic conductivity (K s) and the longitudinal dispersivity (D L) for the different horizons. Model predictions showed only minor improvements over those previously obtained assuming homogeneous soil profiles. In an effort to improve the predictions, we also carried out a two-step, sequential optimization in which we first estimated the soil hydraulic parameters followed by estimation of the solute transport parameters. This approach allowed us to include additional parameters in the optimization process. A sensitivity analysis was performed to determine the most sensitive hydraulic and solute transport parameters. Soil water contents were found to be most sensitive to the n parameter in van Genuchten's soil hydraulic model, followed by the saturated water content (q s), while solute concentrations were most affected by q s and D L. For these reasons, we estimated q s and n for the various soil horizons of the sequential optimization process during the first step, and only D L during the second step. Sequential estimation somewhat improved predictions of the cumulative infiltration rates during the first irrigation event. It also significantly improved descriptions of the soil water content, particularly of the upper horizons, as compared to those obtained using simultaneous estimation, whereas deep percolation rates of water did not improve. Solute concentrations in the soil profiles were predicted equally well with both optimization approaches.

In a subclass of the scale-parameter exponential family, we consider the sequential point estimation of a function of the scale parameter under the loss function given as the sum of the weighted squared error loss and a linear cost. For a fully sequential sampling scheme, second order expansions are obtained for the expected sample size as well as for the regret of the procedure. The former researches on Gamma and Exponential distributions can be deduced from our general results.

The object of this paper is to produce non-parametric maximum likelihood estimates of forecast distributions in a general non-Gaussian, non-linear state space setting. The transition densities that de…ne the evolution of the dynamic state process are represented in parametric form, but the conditional distribution of the non-Gaussian variable is estimated non-parametrically. The …ltering and prediction distributions are estimated via a computationally e¢ cient algorithm that exploits the functional relationship between the observed variable, the state variable and a measurement error with an invariant distribution. Simulation experiments are used to document the accuracy of the non-parametric method relative to both correctly and incorrectly speci…ed parametric alternatives. In an empirical illustration, the method is used to produce sequential estimates of the forecast distribution of realized volatility on the S&P500 stock index during the recent …nancial crisis. A resampling technique for measuring sampling variation in the estimated forecast distributions is also demonstrated.

This paper reviews methods for the estimation of dynamic discrete choice structural models and discusses related econometric issues. We consider single agent models, competitive equilibrium models and dynamic games. The methods are illustrated with descriptions of empirical studies which have applied these techniques to problems in different areas of economics. Programming codes for the estimation methods will be available in a companion web page.

This paper proposes a procedure for the estimation of discrete Markov decision models and studies its statistical and computational properties. Our Nested Pseudo-Likelihood method (NPL) is similar to Rust's Nested Fixed Point algorithm (NFXP), but the order of the two nested algorithms is swapped. First, we prove that NPL produces the Maximum Likelihood Estimator under the same conditions as NFXP. Our procedure requires fewer policy iterations at the expense of more likelihood-climbing iterations. We focus on a class of in…nite-horizon, partial likelihood problems for which NPL results in large computational gains. Second, based on this algorithm we de…ne a class of consistent and asymptotically equivalent Sequential Policy Iteration (PI) estimators, which encompasses both Hotz-Miller's CCP estimator and the partial Maximum Likekihood estimator. This presents the researcher with a "menu" of sequential estimators re ‡ecting a trade-o¤ between …nite-sample precision and computational cost. Using actual and simulated data we compare the relative performance of these estimators. In all our experiments the bene…ts in terms of precision of using a 2-stage PI estimator instead of 1-stage (i.e., Hotz-Miller) are very signi…cant. More interestingly, the bene…ts of MLE relative to 2-stage PI are small.

This paper studies the estimation of dynamic discrete games of incomplete information. Two main econometric issues appear in the estimation of these models: the indeterminacy problem associated with the existence of multiple equilibria, and the computational burden in the solution of the game. We propose a class of pseudo maximum likelihood (PML) estimators that deals with these problems and we study the asymptotic and finite sample properties of several estimators in this class. We first focus on two-step PML estimators which, though attractive for their computational simplicity, have some important limitations: they are seriously biased in small samples; they require consistent nonparametric estimators of players' choice probabilities in the first step, which are not always feasible for some models and data; and they are asymptotically inefficient. Second, we show that a recursive extension of the two-step PML, which we call nested pseudo likelihood (NPL), addresses those drawbacks at a relatively small additional computational cost. The NPL estimator is particularly useful in applications where consistent nonparametric estimates of choice probabilities are either not available or very imprecise, e.g., models with permanent unobserved heterogeneity. Finally, we illustrate these methods in Montecarlo experiments and in an empirical application to a model of firm entry and exit in oligopoly markets using Chilean data from several retail industries.

The propagation of bottom and oceanographic variability through to the variability of acoustic transmissions and reverberation is evaluated with a simple adiabatic model interacting with Gaussian distributed uncertainty in a narrow frequency band. Results show that there is significant sensitivity of time series and reverberation uncertainty to different types of environmental uncertainty. For propagation over uncertain bottoms, it is shown that it is that later part of the time series, corresponding to the highest angle energy reflecting most often off the surface and bottom, that is most sensitive to bottom uncertainty. This implies that the larger reverberation contributions from the highest grazing angles with the largest scattering strength is also the most uncertain. Conversely, it is the lowest angle arrivals which are most sensitive to uncertainty in the sound-speed profile. These behaviors are predicted analytically by the theory [K.D. LePage, in "Impact of Littoral Environmental Variability on Acoustic Predictions and Sonar Performance," Kluwer, 2002, pp. 353-360].

Managing telecommunication networks involves collecting and analyzing large amounts of statistical data. The standard approach to estimating quantiles involves capturing all the relevant data (what may require significant storage/processing capacities), and performing an off-line analysis (what may delay management actions). It is often essential to estimate quantiles as the data are collected, and to take management actions promptly. Towards this goal, we present a minimalist approach to sequentially estimating constant/changing over time quantiles. We follow prior work and devise a fixed-point algorithm, which does not estimate the unknown probability density function at the quantile. Instead, our algorithm uses the log-odds transformation of the observed fractions, and the exponentially smoothed estimates of the standard deviation to update the quantile estimate. For large data streams, this algorithm can significantly reduce the amount of collected data and the complexity of data analysis.

In this paper we propose a Libor model with a high-dimensional specially structured system of driving CIR volatility processes. A stable calibration procedure which takes into account a given local correlation structure is presented. The calibration algorithm is FFT based, so fast and easy to implement.

The problem of pricing Bermudan options using Monte Carlo and a nonparametric regression is considered. We derive optimal nonasymptotic bounds for a lower biased estimate based on the suboptimal stopping rule constructed using some estimates of continuation values. These estimates may be of different nature, they may be local or global, with the only requirement being that the deviations of these estimates from the true continuation values can be uniformly bounded in probability. As an illustration, we discuss a class of local polynomial estimates which, under some regularity conditions, yield continuation values estimates possessing this property.

This paper presents a real-time vision-based system to assist a person with dementia wash their hands. The system uses only video inputs, and assistance is given as either verbal or visual prompts, or through the enlistment of a human caregiver's help. The system combines a Bayesian sequential estimation framework for tracking hands and towel, with a decision theoretic framework for computing policies of action. The decision making system is a partially observable Markov decision process, or POMDP. Decision policies dictating system actions are computed in the POMDP using a point-based approximate solution technique. The tracking and decision making systems are coupled using a heuristic method for temporally segmenting the input video stream based on the continuity of the belief state. A key element of the system is the ability to estimate and adapt to user psychological states, such as awareness and responsiveness. We evaluate the system in three ways. First, we evaluate the hand-tracking system by comparing its outputs to manual annotations and to a simple hand-detection method. Second, we test the POMDP solution methods in simulation, and show that our policies have higher expected return than five other heuristic methods. Third, we report results from a ten-week trial with seven persons moderate-to-severe dementia in a long-term care facility in Toronto, Canada. The subjects washed their hands once a day, with assistance given by our automated system, or by a human caregiver, in alternating two-week periods. We give two detailed case study analyses of the system working during trials, and then show agreement between the system and independent human raters of the same trials.

Acoustic prediction for future time frames usually suffer from uncertainties in ocean forecasts, due to the extreme sensitivity of acoustic propagation to the ocean environment. The current work assesses the feasibility of combining a Feature-Oriented Regional Modeling System (FORMS) with acoustic inversion outcomes, for acoustic prediction in the Cabo Frio (Brazil) coastal area. First, the oceanographic prediction model is tested for acoustic applications. Two numerical acoustic simulations were performed, with an acoustic model having as input two different initial fields: i) in situ hydrographic data from the OAEx10 sea trial, and ii) the oceanographic modeling system outputs. The simulations were compared in terms of transmission loss (TL), detection probability and impulse response. The second stage of this work concerned acoustic data-model comparison, for OAEx10. Experimental impulse responses correlated fairly well with modeled ones corresponding to the forecasts, with values between 0.72 and 0.89. In an attempt to increase these values, the acoustic data was inverted, for the basement compressional speed, whose estimates led to increased impulse response correlations of as high as 0.96. In summary, the prediction of the acoustic field can be well accomplished by combining a FORMS technique with an acoustic inversion scheme.

A recursive estimator of the conditional geometric median in Hilbert spaces is studied. It is based on a stochastic gradient algorithm whose aim is to minimize a weighted L 1 criterion and is consequently well adapted for robust online estimation. The weights are controlled by a kernel function and an associated bandwidth. Almost sure convergence and L 2 rates of convergence are proved under general conditions on the conditional distribution as well as the sequence of descent steps of the algorithm and the sequence of bandwidths. Asymptotic normality is also proved for the averaged version of the algorithm with an optimal rate of convergence. A simulation study confirms the interest of this new and fast algorithm when the sample sizes are large. Finally, the ability of these recursive algorithms to deal with very high-dimensional data is illustrated on the robust estimation of television audience profiles conditional on the total time spent watching television over a period of 24 hours.

With the progress of measurement apparatus and the development of automatic sensors it is not unusual anymore to get large samples of observations taking values in high dimension spaces such as functional spaces. In such large samples of high dimensional data, outlying curves may not be uncommon and even a few individuals may corrupt simple statistical indicators such as the mean trajectory. We focus here on the estimation of the geometric median which is a direct generalization of the real median in metric spaces and has nice robustness properties. The geometric median being defined as the minimizer of a simple convex functional that is differentiable everywhere when the distribution has no atom, it is possible to estimate it with online gradient algorithms. Such algorithms are very fast and can deal with large samples. Furthermore they also can be simply updated when the data arrive sequentially. We state the almost sure consistency and the L 2 rates of convergence of the stochastic gradient estimator as well as the asymptotic normality of its averaged version. We get that the asymptotic distribution of the averaged version of the algorithm is the same as the classic estimators which are based on the minimization of the empirical loss function. The performances of our averaged sequential estimator, both in terms of computation speed and accuracy of the estimations, are evaluated with a small simulation study. Our approach is also illustrated on a sample of more than 5000 individual television audiences measured every second over a period of 24 hours.

Qiu and Sheng has proposed a powerful and robust two-stage procedure to compare two hazard rate functions. In this paper we improve their method by using the Fisher test to combine the asymptotically independent p-values obtained from the two stages of their procedure. In addition, we extend the procedure to situations with multiple hazard rate functions. Our comprehensive simulation study shows that the proposed method has a good performance in terms of controlling the type I error rate and of detecting power. Two real data applications are considered for illustrating the use of the new method.