Stochastic Restricted Biased Estimators in misspecified regression model with incomplete prior information

TL;DR

This paper extends the analysis of stochastic restricted biased estimators to misspecified regression models with multicollinearity and incomplete prior information, comparing their performance through theoretical conditions and simulations.

Contribution

It introduces and evaluates several stochastic restricted biased estimators in misspecified models, providing superiority conditions and empirical validation.

Findings

Certain estimators outperform others in MSEM under specific conditions

Theoretical superiority conditions are established for estimator selection

Simulation results support the theoretical comparisons

Abstract

In this article, 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 (SRPCR), Stochastic Restricted r-k class estimator (SRrk) and Stochastic Restricted r-d class estimator (SRrd) 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.