A Partial Robustifying Weighted Least Squares Estimator

Abstract

The objective of this study is to introduce an alternative weighted least squares estimator called a partial robustifying weighted least squares (RWLS2) estimator. The weight is coincided with the weight of robustifying weighted least squares (RWLS1) estimator proposed by Gulasirima and Siripanich [3] but is partially applied on residuals. Based on ideas of Windham [7] and Gervini and Yohai [2], the proposed weight function is assigned to be one for good observations and less than one for outliers or influential observations. In particular the weight is a proportion of a power of density of errors. RWLS2 is an alternative robust regression estimator which accommodates outliers whilst all assumptions are retained.

The weighted normal random variable has an invariance property with zero mean and decreasing variance. By the results of real data study, it is found that the proposed weight can reduce the effect of influential outliers. RWLS2 performs as well as RWLS1 by mean of R2 but slightly better by means of relative efficiency based on the MSE of least squares (LS) estimator. Both estimators work as well as the LS in situation of no outlier but obviously better when outliers exist.