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

Kaçıranlar, and Sakallıoğlu, [2001. Combining the Liu estimator and the principal component regression estimator. Comm. Statist. Theory Methods 30, 2699–2705] introduced the r-dr-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-dr-d class estimator over each of these estimators and the r-kr-k class estimator by the matrix mean square error (MMSE) criterion. Also, we suggest tests to verify if these conditions are indeed satisfied.