Superiority of the r - d class estimator over some estimators by the mean square error matrix criterion

Kaçi{dotless}ranlar, and Sakalli{dotless}oglu, [2001. Combining the Liu estimator and the principal component regression estimator. Comm. Statist. Theory Methods 30, 2699-2705] introduced the r - d class estimator which is a general estimator of the ordinary least squares (OLS), the principal components regression (PCR) and the Liu estimators. In this paper, we derive conditions for the superiority of the r - d class estimator over each of these estimators and the r - k class estimator by the matrix mean square error (MMSE) criterion. Also, we suggest tests to verify if these conditions are indeed satisfied. © 2006 Elsevier B.V. All rights reserved.FEF2006D7The authors are grateful to the editor and the referee for valuable comments which improved an earlier draft of this paper. The first author was supported by the Scientific and Technical Research Council of Turkey (TUBITAK)-Scientific Human Resources Development (BIDEB). This research was supported by Cukurova University Academic Research Projects under project number FEF2006D7