ESTIMATION IN LINEAR MODELS WITH RANDOM EFFECTS AND ERRORS-IN-VARIABLES

XU-PING ZHONG^{1}, WING-KAM FUNG^{2} AND BO-CHENG WEI^{1}

1Department of Mathematics, Southeast University, Nanjing 210018, China, e-mail: bcw@seu.edu.cn

2Department of Statistics and Actuarial Science, The University of Hong Kong, Pokfulam Road, Hong Kong, China, e-mail: wingfung@hku.hk

(Received July 18, 2000; revised March 29, 2001)

Abstract. The independent variables of linear mixed models are subject to measurement errors in practice. In this paper, we present a unified method for the estimation in linear mixed models with errors-in-variables, based upon the corrected score function of Nakamura (1990, Biometrika, 77, 127–137). Asymptotic normality properties of the estimators are obtained. The estimators are shown to be consistent and convergent at the order of n^{−1/2}. The performance of the proposed method is studied via simulation and the analysis of a data set on hedonic housing prices.

Key words and phrases: Corrected score function, errors-in-variable, fixed effects, random effects, measurement errors.