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, …