Combining two-parameter and principal component regression estimators

This paper is concerned with the parameter estimation in linear regression model. To overcome the multicollinearity problem, a new class of estimator, namely principal component two-parameter (PCTP) estimator is proposed. The superiority of the new estimator over the principal component regression (PCR) estimator, the r − k class estimator, the r − d class estimator and the two-parameter estimator proposed by Yang and Chang (Commun Stat Theory Methods 39:923–934 2010 ) are discussed with respect to the mean squared error matrix (MSEM) criterion. Furthermore, we give a numerical example and a simulation study to illustrate some of the theoretical results.