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

Abstract

The analysis of misspecification was extended to the recently introduced stochastic restricted biased estimators when multicollinearity exists among the explanatory variables. The Stochastic Restricted Ridge Estimator (SRRE), Stochastic Restricted Almost Unbiased Ridge Estimator (SRAURE), Stochastic Restricted Liu Estimator (SRLE), Stochastic Restricted Almost Unbiased Liu Estimator (SRAULE), Stochastic Restricted Principal Component Regression Estimator (SRPCRE), Stochastic Restricted r-k (SRrk) class estimator, and Stochastic Restricted r-d (SRrd) class estimator were examined in the misspecified regression model due to missing relevant explanatory variables when incomplete prior information of the regression coefficients is available. Further, the superiority conditions between estimators and their respective predictors were obtained in the mean square error matrix (MSEM) sense. Finally, a numerical example and a Monte Carlo simulation study were used to illustrate the theoretical findings.

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

“…By following Kayanan and Wijekoon [25], the generalized form to represent the stochastic restricted estimators SRRE, SRAURE, SRLE, SRAULE, SRPCR, SRrk and SRrd for model (28) is given bŷ…”

“…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…”

“…Further, Hubert and Wijekoon [9] discussed the performance of SRLE over the MRE in the misspecified model. Kayanan and Wijekoon [25] examined the performance of SRRE, SRAURE, SRAULE, SRPCRE, SRrk and SRrd over the other existing estimators in the misspecified regression model. These studies have shown that SRLE and SRRE outperformed the other stochastic restricted estimators in the misspecified regression model for the selected range of shrinkage parameters when multicollinearity exists among the regressor variables.…”