Combining the unrestricted estimators into a single estimator and a simulation study on the unrestricted estimators

Abstract

The purpose of this paper is to combine several regression estimators (ordinary least squares (OLS), ridge, contraction, principal components regression (PCR), Liu, r−k and r−d class estimators) into a single estimator. The conditions for the superiority of this new estimator over the PCR, the r−k class, the r−d class, βˆ(k, d), OLS, ridge, Liu and contraction estimators are derived by the scalar mean square error criterion and the estimators of the biasing parameters for this new estimator are examined. Also, a numerical example based on Hald data and a simulation study are used to illustrate the results.

Keywords:

• multicollinearity
• biased estimators
• mean square error

AMS Subject Classification :

• 62J05
• 62J07