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


Ozkale M. R. , Kaciranlar S.

STATISTICS & PROBABILITY LETTERS, vol.77, no.4, pp.438-446, 2007 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 77 Issue: 4
  • Publication Date: 2007
  • Doi Number: 10.1016/j.spl.2006.08.012
  • Title of Journal : STATISTICS & PROBABILITY LETTERS
  • Page Numbers: pp.438-446
  • Keywords: r-d class estimator, ordinary least squares estimator, principal components regression estimator, Liu estimator, r-k class estimator, multicollinearity, PRINCIPAL COMPONENT REGRESSION, COMBINING RIDGE, LIU ESTIMATOR

Abstract

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

Kaciranlar, and Sakalhoglu, [2001. Combining the Liu estimator and the principal component regression estimator. Comm. Statist. Theory Methods 30, 2699-2705] introduced the r-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-d class estimator over each of these estimators and the r-k class estimator by the matrix mean square error (MMSE) criterion. Also, we suggest tests to verify if these conditions arc indeed satisfied. (c) 2006 Elsevier B.V. All rights reserved.