Modified One-Parameter Liu Estimator for the Linear Regression Model

Adewale F Lukman,Segun L Jegede,Kayode Ayinde,B M Golam Kibria

doi:10.1155/2020/9574304

Abstract

Motivated by the ridge regression (Hoerl and Kennard, 1970) and Liu (1993) estimators, this paper proposes a modified Liu estimator to solve the multicollinearity problem for the linear regression model. This modification places this estimator in the class of the ridge and Liu estimators with a single biasing parameter. Theoretical comparisons, real-life application, and simulation results show that it consistently dominates the usual Liu estimator. Under some conditions, it performs better than the ridge regression estimators in the smaller MSE sense. Two real-life data are analyzed to illustrate the findings of the paper and the performances of the estimators assessed by MSE and the mean squared prediction error. The application result agrees with the theoretical and simulation results.

Highlights

Where yn×1 is a vector of the predictand, Xn×p is a known matrix of predictor variables, θp×1 is a vector of unknown regression parameters, ∈n×1 is a vector of errors such that E ð∈Þ = 0 and VðεÞ = σ2 In, and In is an n × n identity matrix
In most real-life applications, we observed that the predictor variables grow together, which result in the problem termed multicollinearity
Since we want to compare the performance of the proposed estimator with the usual Liu and ridge regression estimators, we will give a brief description of each of them as follows

Summary

Introduction

In most real-life applications, we observed that the predictor variables grow together, which result in the problem termed multicollinearity The consequence of this on the OLS estimator is that it reduces its efficiency and it became unstable (for examples, [1, 2]). The objective of this paper is to propose a new oneparameter Liu-type estimator for the regression parameter when the predictor variables of the model are linearly related. Since we want to compare the performance of the proposed estimator with the usual Liu and ridge regression estimators, we will give a brief description of each of them as follows. To compare the performance of the estimators, we will consider the linear regression model in canonical form, which is given as follows:.

The Proposed Estimator and OLSE

The Proposed Estimator and RRE

The Proposed Estimator and Liu Estimator

Simulation Study

Applications

Some Concluding Remarks