Robust Wild Bootstrap for Stabilizing the Variance of Parameter Estimates in Heteroscedastic Regression Models in the Presence of Outliers

TLDR

Bootstrap techniques are widely used across fields such as engineering, physics, meteorology, medicine, biology, and chemistry, and empirical evidence shows they yield efficient estimates under heteroscedasticity. This paper examines the robustness of Wu and Liu’s Wild Bootstrap techniques and proposes a Robust Wild Bootstrap to stabilize regression estimate variance when heteroscedasticity and outliers coexist. The method uses weighted residuals incorporating an MM estimator, robust location and scale, and the Wu–Liu bootstrap sampling scheme. In the presence of outliers, the original techniques lose efficiency, but the proposed Robust Wild Bootstrap outperforms existing methods in all respects.

Abstract

Nowadays bootstrap techniques are used for data analysis in many other fields like engineering, physics, meteorology, medicine, biology, and chemistry. In this paper, the robustness of Wu (1986) and Liu (1988)′s Wild Bootstrap techniques is examined. The empirical evidences indicate that these techniques yield efficient estimates in the presence of heteroscedasticity problem. However, in the presence of outliers, these estimates are no longer efficient. To remedy this problem, we propose a Robust Wild Bootstrap for stabilizing the variance of the regression estimates where heteroscedasticity and outliers occur at the same time. The proposed method is based on the weighted residuals which incorporate the MM estimator, robust location and scale, and the bootstrap sampling scheme of Wu (1986) and Liu (1988). The results of this study show that the proposed method outperforms the existing ones in every respect.