A comparative study of some robust ridge and liu estimators

Abstract

In multiple linear regression analysis, multicollinearity and outliers are two main problems. When multicollinearity exists, biased estimation techniques such as Ridge and Liu Estimators are preferable to Ordinary Least Square. On the other hand, when outliers exist in the data, robust estimators like M, MM, LTS and S Estimators, are preferred. To handle these two problems jointly, the study combines the Ridge and Liu Estimators with Robust Estimators to provide Robust Ridge and Robust Liu estimators respectively. The Mean Square Error (MSE) criterion was used to compare the performance of the estimators. Application to the proposed estimators to three (3) real life data set with multicollinearity and outliers problems reveals that the M-Liu and LTS-Liu Estimator are generally most efficient..

Keywords: Ordinary Least Squares, Ridge Regression Estimator, Liu Estimator, Robust Estimator, Robust Ridge Regression Estimator, Robust Liu Estimator