Özet:
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 (Formula presented.) is partitioned into two parts, namely, the main effects (Formula presented.) and the nuisance effects (Formula presented.) such that (Formula presented.). 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 (Formula presented.) when (Formula presented.) 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. © 2022 Informa UK Limited, trading as Taylor & Francis Group.