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

Abstract

Consider the linear regression model in the usual notation. In the presence of multicollinearity certain biased estimators like the ordinary ridge regression estimator and the Liu estimator 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.

Keywords:

• Correlation matrix
• Liu estimator
• Mean square error
• Multicollinearity
• Ridge regression estimator

Acknowledgment

The authors are thankful to an anonymous referee for the useful comments and suggestions.