Linear Programming-Based Estimators in Simple Linear Regression

Applications of Mathematics, 1999

Institute of Mathematics of the Academy of Sciences of the Czech Republic provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use. This paper has been digitized, optimized for electronic delivery and stamped with digital signature within the project DML-CZ: The Czech Digital Mathematics Library http://project.dml.cz

Applications of Mathematics

Institute of Mathematics of the Academy of Sciences of the Czech Republic provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use. This paper has been digitized, optimized for electronic delivery and stamped with digital signature within the project DML-CZ: The Czech Digital Mathematics Library http://project.dml.cz 44 (1999) APPLICATIONS OF MATHEMATICS No. 5, 359-374

Metrika, 1986

Royall and Herson considered balanced samples for ensuring robustness of standard ratio estimator under polynomial superpopulation models. Here we formulate a post-sample estimator of Royall type which remains robust (in respect of bias) under a wide class of polynomial regression models.

Biometrical Journal, 1984

Thie note points out the derivation of regression estimator through an optimality consideration over a c~ass of eetimatora generating Generalised Product and dual to ratio eatimators.

Linear Algebra and its Applications, 1992

Minimax-linear estimation with respect to the quadratic risk is considered among the class of linear estimators of p, under the linear regression model M = {y, XI3, (r'1). New classes of minimax-linear estimators of I3 are derived among certain subsets of linear estimators, which are simple from the point of view of minimax estimation. The admissible linear estimators of I3 under M are then characterized via these classes of minimax-linear estimators, and the relationship between the minimax-linear and admissible estimators of p is examined. Various properties of linear admissible estimators follow readily from this new characterization.

Global Journal of Pure and Applied Sciences, 2008

In linear regression model, regressors are assumed fixed in repeated sampling. This assumption is not always satisfied especially in business, economics and social sciences. Consequently in this paper, effort is made to compare the performances of some estimators of linear model with autocorrelated error terms when normally distributed regressors are fixed (non-stochastic) with when they are stochastic. The estimators are the ordinary least square (OLS) estimator and four feasible generalized least estimators which are Cochrane Orcutt (CORC), Hidreth-Lu (HILU), Maximum Likelihood (ML), Maximum Likelihood Grid (MLGD) estimator. These estimators are compared using the finite properties of estimators' criteria namely; sum of biases, sum of variances and sum of the mean squared error of the estimated parameter of the model at different levels of autocorrelation and sample size through Monte-Carlo studies.

Stats, 2025

We propose an unbiased restricted estimator that leverages prior information to enhance estimation efficiency for the linear regression model. The statistical properties of the proposed estimator are rigorously examined, highlighting its superiority over several existing methods. A simulation study is conducted to evaluate the performance of the estimators, and real-world data on total national research and development expenditures by country are analyzed to illustrate the findings. Both the simulation results and real-data analysis demonstrate that the proposed estimator consistently outperforms the alternatives considered in this study.

Annals of the Institute of Statistical …, 1992

In linear regression models with random coefficients, the score function usually involves unknown nuisance parameters in the form of weights. Conditioning with respect to the sufficient statistics for the nuisance parameter, when the parameter of interest is held fixed, eliminates the nuisance parameters and is expected to give reasonably good estimating functions. The present paper adopts this approach to the problem of estimation of average slope in random coefficient regression models. Four sampling situations axe discussed. Some asymptotic results are also obtained for a model where neither the regressors nor the random regression coefficients replicate. Simulation studies for normal as well as non-normal models show that the performance of the suggested estimating functions is quite satisfactory.

Statistics & Probability Letters, 1999

This note considers a paradox arising in the least-squares estimation of linear regression models in which the error terms are assumed to be i.i.d. and possess ÿnite rth moment, for r ∈ [1; 2). We give a concrete example to show that the least-squares estimator of the slope parameter is inconsistent when the intercept parameter of the model is given. However, surprisingly this estimator is consistent when the intercept parameter is intendedly assumed to be unknown and re-estimated simultaneously with the slope parameter.

The Japanese Economic Review, 1997

Two approaches have been developed for deriving the properties of ef®ciency and consistency of standard errors of two step estimators of linear models containing current or lagged unobserved expectations of a single variable. One method is based on the derivatives of the likelihood function and information matrix, while the other uses the true covariance matrix of the disturbance vector when unknown parameters or variables are replaced by corresponding estimates. In this paper, the second approach is extended to cases where the structural equation is nonlinear and the model contains expectations of more than one variable or expectations of future variables. The properties of a frequently used estimator to deal with missing observations problems, a model involving a variance as an explanatory variable, and a recently developed estimator for autoregressive moving average models can be easily derived using the results of the paper. Methods for improving the ef®ciency of two step estimators are outlined.