Comparisons of the unbiased ridge estimation to the other estimations


Ozkale M. R. , Kaciranlar S.

COMMUNICATIONS IN STATISTICS-THEORY AND METHODS, vol.36, pp.707-723, 2007 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 36
  • Publication Date: 2007
  • Doi Number: 10.1080/03610920601033652
  • Title of Journal : COMMUNICATIONS IN STATISTICS-THEORY AND METHODS
  • Page Numbers: pp.707-723
  • Keywords: multicollinearity, ordinary least squares estimator, ordinary ridge regression estimator, residual, r - k class estimator, unbiased ridge regression estimator, PRIOR INFORMATION, LINEAR-REGRESSION

Abstract

In the presence of multicollinearity, ordinary least squares (OLS) estimation is inadequate. Alternative estimation techniques were proposed. One of which is unbiased ridge regression (URR) estimator given by Crouse et al. (1995). In this article, we introduced the URR estimator in two different ways by following Farebrother (1984) and Troskie et al. (1994). We discuss its properties in some detail, comparing URR estimator to the OLS, the ordinary ridge regression (ORR), and the r − k class estimators in the sense of matrix mean square error (MMSE) and residuals. We also illustrate our findings with a numerical example based on the data generated by Hoerl and Kennard (1981) which is commonly used in literature to study the effect of multicollinearity.

In the presence of multicollinearity, ordinary least squares (OLS) estimation is inadequate. Alternative estimation techniques were proposed. One of which is unbiased ridge regression (URR) estimator given by Crouse et al. (1995). In this article, we introduced the URR estimator in two different ways by following Farebrother (1984) and Troskie et al. (1994). We discuss its properties in some detail, comparing URR estimator to the OLS, the ordinary ridge regression (ORR), and the r - k class estimators in the sense of matrix mean square error (MMSE) and residuals. We also illustrate our findings with a numerical example based on the data generated by Hoerl and Kennard (1981) which is commonly used in literature to study the effect of multicollinearity.