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

Abstract

In this article, we propose the Sample Information Optimal Estimator (SIOE) and the Stochastic Restricted Optimal Estimator (SROE) for misspecified linear regression model when multicollinearity exists among explanatory variables. Further, we obtain the superiority conditions of proposed estimators over some other existing estimators in the Mean Square Error Matrix (MSEM) criterion in a standard form which can apply to all estimators considered in this study. Finally, a real-world example and a Monte Carlo simulation study are presented for the proposed estimators to illustrate the theoretical results.

Generalized Stochastic Restricted LARS Algorithm

“…The biased estimators such as Ridge Estimator (RE) (Hoerl and Kennard 1970), Almost Unbiased Ridge Estimator (AURE) (Singh et al 1986), Liu Estimator (LE) (Liu 1993), Almost Unbiased Liu Estimator (AULE) (Akdeniz and Kaçiranlar 1995), Principle Component Regression Estimator (PCRE) (Massy 1965), r-k class estimator (Baye and Parker 1984), r-d class estimator (Kaçiranlar and Sakallıoğlu 2001) and Sample Information Optimal Estimator (SIOE) (Kayanan and Wijekoon 2019) have been widely used in literature to resolve multicollinearity issue in the linear regression model. However, these estimators yield high bias when the number of explanatory variables is high, and they do not consider about irrelevant variables while fitting models.…”

“…The prior information on regression coefficients can be defined in the form of exact linear restrictions or stochastic linear restrictions. Many researchers proposed stochastic restricted estimators such as Mixed Regression Estimator (MRE) (Theil and Goldberger 1961) Stochastic Restricted Ridge Estimator (SRRE) (Li and Yang 2010) (Kayanan and Wijekoon 2019) to incorporate prior information to the regression coefficient. Stochastic restricted estimators also have the same issue as biased estimators when the linear regression model contains numerous predictors.…”