Comparisons of the Unbiased Ridge Estimation to the Other Estimations

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.

Keywords:

• Multicollinearity
• Ordinary least squares estimator
• Ordinary ridge regression estimator
• Residual
• r − k class estimator
• Unbiased ridge regression estimator

Mathematics Subject Classification:

• Primary 62J05
• Secondary 62J07

Acknowledgment

The authors are grateful to the editor and the referee for valuable comments which improved an earlier draft of this article.