Liu-type Shrinkage Estimations in Linear Models

TL;DR

This paper introduces Liu-type shrinkage estimators for linear models with partitioned parameters, focusing on estimating main effects when nuisance effects are near zero, and demonstrates their efficiency through Monte Carlo simulations.

Contribution

It proposes new Liu-type estimators for linear models with partitioned parameters and evaluates their performance via simulation, showing their superiority.

Findings

Proposed estimators outperform traditional methods in simulations.

Liu-type estimators effectively estimate main effects when nuisance effects are small.

Simulation results confirm the efficiency of the new estimators.

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.