The new mixed ridge estimator in a linear mixed model with measurement error under stochastic linear mixed restrictions

Abstract

In this paper, we propose a new ridge type estimator, called a new mixed ridge estimator (NMRE) in the linear mixed model (LMM) with the measurement error when the stochastic restrictions are available on fixed and random effect and the fixed effect variables are multicollinear. The new estimator is a generalization of the ridge estimator (RE) and mixed estimator (ME). Then, asymptotic normality properties of these estimators will be derived and the necessary and sufficient conditions for the superiority of the NMRE over the RE and ME are obtained by using the mean squared error matrix. Finally, the theoretical findings of the proposed estimator are illustrated by using a data example and a Monte Carlo simulation.

Keywords:

• Multicollinearity
• Measurement error
• Nakamura’s approach
• Mixed estimator
• Mixed ridge estimator

Acknowledgments

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