A Class of s-K Type Principal Components Estimators in the Linear Model

In this article, we introduce a new class of estimators called the s-K type principal components estimators to combat multicollinearity, which include the principal components regression (PCR) estimator, the r-k estimator and the s-K estimator as special cases. Necessary and sufficient conditions for the superiority of the new estimator over the PCR estimator, the r-k estimator and the s-K estimator are derived in the sense of the mean squared error matrix criterion. A Monte Carlo simulation study and a numerical example are given to illustrate the performance of the proposed estimator.