Performance of Existing Biased Estimators and the Respective Predictors in a Misspecified Linear Regression Model

Abstract

In this paper, the performance of existing biased estimators (Ridge Estimator (RE), Almost Unbiased Ridge Estimator (AURE), Liu Estimator (LE), Almost Unbiased Liu Estimator (AULE), Principal Component Regression Estimator (PCRE), r-k class estimator and r-d class estimator) and the respective predictors were considered in a misspecified linear regression model when there exists multicollinearity among explanatory variables. A generalized form was used to compare these estimators and predictors in the mean square error sense. Further, theoretical findings were established using mean square error matrix and scalar mean square error. Finally, a numerical example and a Monte Carlo simulation study were done to illustrate the theoretical findings. The simulation study revealed that LE and RE outperform the other estimators when weak multicollinearity exists, and RE, r-k class and r-d class estimators outperform the other estimators when moderated and high multicollinearity exist for certain values of shrinkage parameters, respectively. The predictors based on the LE and RE are always superior to the other predictors for certain values of shrinkage parameters.

Optimal estimators in misspecified linear regression model with an application to real-world data

“…According to Kayanan and Wijekoon [18], the generalized form to represent the estimators RE, AURE, LE, AULE, PCR, r−k class estimator and r−d class estimator for model ( 24) is given by γG = Gγ OLSE (26) where…”

“…Note that, γ G = γG when G = G and γ = γ, and γ G = γ * G when G = G * and γ = γ * . According to Kayanan and Wijekoon [18,25], the bias vector, dispersion matrix and MSEM of γ G can be presented as…”

“…Şiray [15], Wu [16] and Chandra and Tyagi [17] examined the efficiency of the r-d class estimator and r-k class estimator over some existing estimators in the misspecified regression model. Recently, Kayanan and Wijekoon [18] studied the performance RE, AURE, LE, AULE, PCRE, r-k class estimator and r-d class estimator in the misspecified linear regression model. These studies have shown that r-d class estimator and r-k class estimator outperformed the other biased estimators in the misspecified regression model for the selected range of shrinkage parameters when multicollinearity exists among the regressor variables.…”

Variable Selection via Biased Estimators in the Linear Regression Model

“…In recent studies, Kayanan and Wijekoon [8] have shown that r-k class estimator and r-d class estimator outperformed other estimators for the selected range of regularization parameter values when multicollinearity exists among the predictor variables. However, biased estimators introduce heavy bias when the number of predictor variables is high, and the final model may contain some irrelevant predictor variables as well.…”

Stochastic Restricted Biased Estimators in Misspecified Regression Model with Incomplete Prior Information

“…Chandra and Tyagi [4] studied the effect of misspecification due to the omission of relevant variables on the dominance of the -( , ) class estimator. Recently, Kayanan and Wijekoon [5] examined the performance of existing biased estimators and the respective predictors based on the sample information in a misspecified linear regression model without considering any prior information about regression coefficients. It is recognized that the mixed regression estimator (MRE) introduced by Theil and Goldberger [6] outperforms ordinary least squares estimator (OLSE) when the regression model is correctly specified.…”