Improved estimation in elliptical linear mixed measurement error models

Abstract

In this paper, we propose a set of improved estimators for the fixed effect parameters in the linear mixed models when the covariates are measured with additive errors and prior information for the parameters is available. When it is suspected that the parameter vector may be the null-vector with some degree of uncertainty, we define improved estimators which including the preliminary test estimator, the Stein-type estimator and the postive-rule Stein-type estimator. It is assumed that the measurement error distributed according to the law belonging to the class of elliptically contoured distributions. The asymptotic properties of resulting estimators such as the asymptotic distributional quadratic biases and the asymptotic distributional quadratic risks are examined. A simulation study is also performed to illustrate the finite sample performance of the proposed procedures and finally Boston housing data set is analysed.