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 beta is partitioned into two parts, namely, the main effects beta(1) and the nuisance effects beta(2) such that beta = (beta(1), beta(2)). 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 maybe enough for this purpose. Thus, the main interest is to estimate beta(1) when beta(2) 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.