Liu-type shrinkage estimations in linear models

In this study, we present the preliminary test, Stein-type and positive part Stein-type Liu estimators in the linear models when the parameter vector β is partitioned into two parts, namely, the main effects β1 and the nuisance effects β2 such that β=(β1,β2). We consider the case that a priori known or suspected set of the explanatory variables do not contribute to predict the response so that a sub-model may be enough for this purpose. Thus, the main interest is to estimate β1 when β2 is close to zero. Therefore, we investigate the performance of the suggested estimators asymptotically and via a Monte Carlo simulation study. Moreover, we present a real data example to evaluate the relative efficiency of the suggested estimators, where we demonstrate the superiority of the proposed estimators.