Combining Unbiased Ridge and Principal Component Regression Estimators

Abstract

In the presence of multicollinearity problem, ordinary least squares (OLS) estimation is inadequate. To circumvent this problem, two well-known estimation procedures often suggested are the unbiased ridge regression (URR) estimator given by Crouse et al. (1995) and the (r, k) class estimator given by Baye and Parker (1984). In this article, we proposed a new class of estimators, namely modified (r, k) class ridge regression (MCRR) which includes the OLS, the URR, the (r, k) class, and the principal components regression (PCR) estimators. It is based on a criterion that combines the ideas underlying the URR and the PCR estimators. The standard properties of this new class estimator have been investigated and a numerical illustration is done. The conditions under which the MCRR estimator is better than the other two estimators have been investigated.

Keywords:

• (r, k) class estimator
• Multicollinearity
• Ordinary least squares estimator
• Ordinary ridge regression estimator
• Principal components regression estimator
• Unbiased ridge regression estimator

Mathematics Subject Classification:

• 62J05
• 62J07