The weighted ridge estimation for linear mixed models with measurement error under stochastic linear mixed restrictions

Abstract

In this paper, we introduce a new ridge-type estimator/predictor called the weighted mixed ridge estimator/predictor (WMRE/P) by unifying the sample and prior information in a linear mixed model with measurement error on fixed effects, when additional stochastic linear restrictions are assumed to have fixed and random effects. The asymptotic normality property of the proposed estimator will be derived, and the necessary and sufficient conditions for the superiority of the WMRE/P over the weighted mixed estimator/predictor (WME/P) and mixed ridge estimator/predictor (MRE/P) will be obtained in terms of mean square error matrix (MSEM) criterion. Finally, the theoretical findings of the proposed estimator are illustrated using a data example and a Monte Carlo simulation.

Keywords:

• Measurement error
• corrected score function
• multicollinearity
• weighted mixed ridge estimator
• mixed predictor

MATHEMATICS SUBJECT CLASSIFICATION:

• 62J05
• 62J07

Additional information

Funding

The research of Professor S. Ejaz Ahmed was supported by the Natural Sciences and the Engineering Research Council (NSERC) of Canada.