Mean Squared Error Matrix Comparisons of Some Biased Estimators in Linear Regression

摘要

Consider the linear regression model y = Xβ + u in the usual notation. In the presence of multicollinearity certain biased estimators like the ordinary ridge regression estimator β_k = (X′X + kI)~(-1) X′y and the Liu estimator β_d = (X′X + I)~(-1)(X′y + dβ) introduced by Liu (Liu, Ke Jian. (1993). A new class of biased estimate in linear regression. Communications in Statistics-Theory and Methods 22(2):393-402) or improved ridge and Liu estimators are used to outperform the ordinary least squares estimates in the linear regression model. In this article we compare the (almost unbiased) generalized ridge regression estimator with the (almost unbiased) generalized Liu estimator in the matrix mean square error sense.