Liu-type Shrinkage Estimations in Linear Models
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abstract

In this study, we present the preliminary test, Stein-type and positive part
Liu estimators in the linear models when the parameter vector
$\boldsymbol{\beta}$ is partitioned into two parts, namely, the main effects
$\boldsymbol{\beta}_1$ and the nuisance effects $\boldsymbol{\beta}_2$ such
that $\boldsymbol{\beta}=\left(\boldsymbol{\beta}_1, \boldsymbol{\beta}_2
\right)$. 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 $\boldsymbol{\beta}_1$ when $\boldsymbol{\beta}_2$ is close to zero.
Therefore, we conduct a Monte Carlo simulation study to evaluate the relative
efficiency of the suggested estimators, where we demonstrate the superiority of
the proposed estimators.