Effect of Misspecifying the Disturbance Covariance Matrix on a Family of Shrinkage Estimators

Abstract

The present article deals with the problem of misspecifying the disturbance-covariance matrix as scalar, when it is locally non scalar. We consider a family of shrinkage estimators based on OLS estimator and compare its asymptotic properties with the properties of OLS estimator. We proposed a similar family of estimators based on FGLS and compared its asymptotic properties with the shrinkage estimator based on OLS under a Pitman's drift process. The effect of misspecifying the disturbances covariance matrix was analyzed with the help of a numerical simulation.

Keywords:

• Asymptotic distribution
• Linear model
• Non spherical disturbances
• Pitman's drift process
• Risk under quadratic loss
• Shrinkage estimator
• Stein rule estimators

Mathematics Subject Classification:

• 62J05
• 62J07

Acknowledgments

The authors are thankful to Prof. Shalabh for his helpful comments on an earlier draft. The second author gratefully acknowledges the financial support from CSIR to carry out the present work.