Performance of Robust Wild Bootstrap Estimation of Linear Model in the Presence of Outliers and Heteroscedasticity Errors

Abstract

Bootstrap techniques are widely used today in many other fields such as economics, Business Administration, Physics, Engineering, Chemistry, Meteorological, Biological Sciences and Medicine. This paper is concerned with the estimation of linear regression model parameters in the presence of heteroscedasticity using wild bootstrap approaches of Wu and Liu. The empirical evidence has shown that these techniques are effective in the presence of heteroscedasticity. However, when there are outliers in the data, this method is no longer effective. To overcome this situation, this paper proposed robust wild bootstrap estimation methods where heteroscedasticity and outliers occur simultaneously. The proposed method is based on the Tukey-redesceding M-estimator which incorporate the LTS and LMS estimator, robust scale and location, and the wild bootstrap sampling procedures of Liu and Wu. Its performance is compared with other existing robust wild bootstrap estimator of MM-estimator using real data and simulation study. The results obtained from this study disclosed that the proposed methods offer a substantial improvement over the existing techniques and proved to be a good alternative estimator.