New Method for Outlier Diagnostics in Linear Regression

Abstract

The detection of the discordant points, i.e., outliers, in linear regression models is a problem, which has been studied extensively. Huber's M-estimation is recommended not only for robust regression but also for detecting outliers. However, M-estimation does not show high performance in detecting outliers for some cases. The aim of this paper is to propose a new method for improving the ability of M-estimation in outlier detection. It consists of the iterative combination of the M-estimator along with a scheme of reducing weights in some observations at random. The theorems proving contribution of the proposed algorithms have also been included. A series of Monte Carlo simulation experiments show that the performance of the new algorithm in the presence of outliers is better than M-estimation alone. By using the new method, the results, on average, improved by about 7%.