Comparison of the r-(k,d) class estimators to some estimators by the mean square error matrix criteria

The ordinary leastsquares, the principal components regression and the Liu-type estimators are special cases of ther-(k,d)class estimators, for regression models with multicollinearity. In thisa rticle we derived conditions for the superiority of ther-(k,d) classestimatoroverotherestimatorssuch as ordinaryleastsquares, principalcomponentandLiu-typeestimatorbased on the mean square error matrix(MSEM)criterion. Finally, a numericale xample and a Monte Carlo simulation are also given to show the theoretical results