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.
Highlights
Misspecification due to left out relevant explanatory variables is very often when considering the linear regression model, which causes these variables to become a part of the error term
One or more assumptions of the linear regression model will be violated when the model is misspecified, and the estimators become biased and inconsistent. It is well-known that the ordinary least squares estimator (OLSE) may not be very reliable if multicollinearity exists in the linear regression model
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
Summary
Misspecification due to left out relevant explanatory variables is very often when considering the linear regression model, which causes these variables to become a part of the error term. The intention of this work is to examine the performance of the recently introduced stochastic restricted biased estimators in the misspecified regression model with incomplete prior knowledge about regression coefficients when there exists multicollinearity among explanatory variables. 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. The biased estimation with stochastic linear restrictions in the misspecified regression model due to inclusion of an irrelevant variable with the incorrectly specified prior information was discussed by Terasvirta [7]. Later Mittelhammer [8], Ohtani and Honda [9], Kadiyala [10], and Trenkler and Wijekoon [11] discussed the efficiency of MRE under misspecified regression model due to exclusion of a relevant variable with correctly specified prior information. The references and appendixes are given at the end of the paper
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