Performance of Some Stochastic Restricted Ridge Estimator in Linear Regression Model

Jibo Wu,Chaolin Liu

doi:10.1155/2014/508793

Abstract

This paper considers several estimators for estimating the stochastic restricted ridge regression estimators. A simulation study has been conducted to compare the performance of the estimators. The result from the simulation study shows that stochastic restricted ridge regression estimators outperform mixed estimator. A numerical example has been also given to illustrate the performance of the estimators.

Highlights

In regression analysis, researchers often encounter the problem of multicollinearity
We introduce some stochastic restricted ridge estimators for estimating the ridge parameter k based on the work of Hoerl and Kennard [2], Hoerl et al [4], Schaeffer et al [16], Kibria [6], and Kibria et al [7]
With the increasing of observations, the mean squared error (MSE) of stochastic restricted ridge estimator (SRRE) and mixed estimator (ME) are decreasing, SRRE is always better than the ME

Summary

Introduction

Researchers often encounter the problem of multicollinearity. Multicollinearity leads to high variance and instable parameter estimates when estimating linear regression models using ordinary least squares (OLS). Many researchers propose many ways to overcome this problem. One method to overcome multicollinearity is to consider biased estimator, such as principal component regression estimator [1], ridge estimator [2], and Liu estimator (Liu, 1993). Ridge estimator is used by many researchers. When we use ridge estimator, how to choose the parameter k is very important. A lot of ways of estimating the ridge parameter k have been proposed. Hoerl and Kennard [2], Hoerl and Kennard [3], Hoerl et al [4], McDonald and Galarneau [5], Kibria [6], Kibria et al [7], and Najarian et al [8]

Objectives

Methods

Results