M Robust Weighted Ridge Estimator in Linear Regression Model

Abstract

Correlated regressors are a major threat to the performance of the conventional ordinary least squares (OLS) estimator. The ridge estimator provides more stable estimates in this circumstance. However, both OLS and Ridge estimators are sensitive to outlying observations. In previous studies, the robust ridge based on the M estimator suitably fit well to the model with multicollinearity and outliers in outcome variable. Since outlier is one of the sources of heteroscedasticity and the non – robust weighted least squares have been previously adopted to account for it. Therefore, this paper proposed and developed some novel estimators to handle three problems (multicollinearity, heteroscedasticity and outliers) simultaneously with the aim of identifying the most efficient (best) ones. The Ordinary Least Square (OLS) and M robust estimator in two weighted version (real weight (WO) and one estimated weight (W1)) were combined to respectively develop the M Robust Ridge and M Robust Weighted Ridge Estimators. Monte–Carlo simulation experiments were conducted on a linear regression model with three and six explanatory variables exhibiting different degrees of Multicollinearity, with heteroscedasticity structure of powers, magnitude of outlier in y direction and error variances and five levels of sample sizes. The Mean Square Error (MSE) was used as a criterion to evaluate the performances of the new and existing estimators. It is evident from the simulation results that the proposed estimators produced efficient estimates and hereby recommended.

Keywords

• linear regression model, multicollinearity, m estimator, heteroscedasticity