Liu-type shrinkage estimations in linear models

Abstract

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 $\text{β}$ is partitioned into two parts, namely, the main effects ${\text{β}}_1$ and the nuisance effects ${\text{β}}_2$ such that $\text{β}=({\text{β}}_1,{\text{β}}_2)$. 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 may be enough for this purpose. Thus, the main interest is to estimate ${\text{β}}_1$ when ${\text{β}}_2$ 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.

Keywords:

• Sub-model
• full model
• pretest and shrinkage estimation
• penalty estimation
• Monte Carlo simulation

2020 Mathematics Subject Classifications:

• 62J05
• 62J07

This article refers to:

Corrigendum: a note on Liu-type shrinkage estimations in linear models (Statistics 56, 396–420)

This article is referred to by:

Corrigendum: a note on Liu-type shrinkage estimations in linear models (Statistics 56, 396–420)

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The research of S. Ejaz Ahmed was funded by the Natural Sciences and Engineering Research Council of Canada (NSERC).