Robust wild bootstrap for stabilizing the variance of parameter estimates in heteroscedastic regression models in the presence of outliers (Q1955125)

Summary: Nowadays bootstrap techniques are used for data analysis in many fields like engineering, physics, meteorology, medicine, biology, and chemistry. In this paper, the robustness of \textit{C.F.J. Wu} [Ann. Stat. 14, 1261--1295 (1986; Zbl 0618.62072)] and \textit{R.V. Liu}'s [Ann. Stat. 16, No. 4, 1696--1708 (1988; Zbl 0655.62031)] wild bootstrap techniques is examined. Empirical evidence indicats that these techniques yield efficient estimates in the presence of the 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 schemes of the above cited papers. The results of this study show that the proposed method outperforms the existing ones in every respect.