Mean squared error matrix comparisons of some biased estimators in linear regression


Akdeniz F., Erol H.

COMMUNICATIONS IN STATISTICS-THEORY AND METHODS, vol.32, no.12, pp.2389-2413, 2003 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 32 Issue: 12
  • Publication Date: 2003
  • Doi Number: 10.1081/sta-120025385
  • Journal Name: COMMUNICATIONS IN STATISTICS-THEORY AND METHODS
  • Journal Indexes: Science Citation Index Expanded, Scopus
  • Page Numbers: pp.2389-2413

Abstract

Consider the linear regression model y = Xbeta + it in the usual notation. In the presence of multicollinearity certain biased estimators like the ordinary ridge regression estimator (β) over cap (k) = (X'X + kI)X-1'y and the Liu estimator (β) over cap (d) = (X'X + I)(-1)(X'y + d (β) over cap) 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 out-perform 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.