Improved estimation of regression parameters in measurement error models |
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Authors: | HM Kim AKMdEhsanes Saleh |
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Institution: | aDepartment of Public Health Sciences, University of Alberta, Edmonton, Canada;bDepartment of Mathematics and Statistics, Carleton University, Ottawa, Canada K1S 5B6 |
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Abstract: | The problem of simultaneous estimation of the regression parameters in a multiple regression model with measurement errors is considered when it is suspected that the regression parameter vector may be the null-vector with some degree of uncertainty. In this regard, we propose two sets of four estimators, namely, (i) the unrestricted estimator, (ii) the preliminary test estimator, (iii) the Stein-type estimator and (iv) the postive-rule Stein-type estimator. In an asymptotic setup, properties of these estimators are studied based on asymptotic distributional bias, MSE matrices, and risks under a quadratic loss function. In addition to the asymptotic dominance of the Stein-type estimators, the paper contains discussion of dominating confidence sets based on the Stein-type estimation. Asymptotic analysis is considered based on a sequence of local alternatives to obtain the desired results. |
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Keywords: | Linear regression Empirical Bayes Point estimation Confidence regions |
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