Generalized Ridge LAD Estimator in Linear Regression Model

Abstract

The Ordinary Least Squares (OLS) Estimator is the most popularly used estimator to estimate the parameters of linear regression model. The estimator has some very attractive statistical properties which has made it the most powerful estimator of regression model under certain assumptions. However, violations of assumptions such as presence of multicollinearity among explanatory variables, outliers and auto-correlated error term affects the efficiency of the estimator. It has been established in literature that these problems can jointly exist in a dataset. This necessitate the introduction of a new estimator to handle these problems sequentially. Therefore, generalized estimators based on ridge and least absolute deviation (LAD) was proposed to deal with multicollinearity, outliers in the y-direction and autocorrelated error. The performance of the new estimator is compared with some of the existing estimators in terms of their mean square error. RIDGE and GLSRIDGELAD estimators perform consistently better than other estimators when there is multicollinearity and autocorrelated error only. GLSRIDGELAD, RIDGELAD and GLSLAD<strong> </strong>perform consistently better than other estimators when the three problems exist. Finally, the GLSRIDGELAD estimator does reasonably well in either cases.