Improved estimation of regression parameters in measurement error models

• Published in: Journal of multivariate analysis Vol. 95; no. 2; pp. 273 - 300
• Main Authors: Kim, H.M., Saleh, A.K.Md.Ehsanes
• Format: Journal Article
• Language: English
• Published: San Diego, CA Elsevier Inc 01.08.2005; Elsevier; Taylor & Francis LLC
• Series: Journal of Multivariate Analysis
• Subjects: Asymptotic methods; Bias; Confidence regions; Decision theory; Empirical Bayes; Exact sciences and technology; Linear inference, regression; Linear regression; Linear regression Empirical Bayes Point estimation Confidence regions; Mathematics; Multivariate analysis; Parametric inference; Point estimation; Probability and statistics; Regression analysis; Sciences and techniques of general use; Statistics; Studies; Empirical Bayes; Confidence regions; 62J05; Linear regression; Point estimation; 62C12; 62F10; 62F25; 1991 subject classification: 62J05; Parameter estimation; Error estimation; Asymptotic behavior; Risk function; Multiple regression; Empirical Bayes estimation; Mean square error; Statistical method; Loss function; Stein estimator; Confidence set; Asymptotic bias; 62F25 Linear regression; Preliminary test; Measurement error; Biased estimation
• ISSN: 0047-259X; 1095-7243
• DOI: 10.1016/j.jmva.2004.08.007

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.