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Mathematical Problems in Engineering
Volume 2012, Article ID 730328, 14 pages
Research Article

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

1Department of Mathematics, Faculty of Science, Universiti Putra Malaysia, Serdang, 43400 Selangor, Malaysia
2Laboratory of Computational Statistics and Operations Research, Institute for Mathematical Research, Universiti Putra Malaysia, Serdang, Selangor 43400, Malaysia
3Department of Mathematical Sciences, Ball State University, Muncie, IN 47306, USA

Received 31 July 2011; Revised 31 October 2011; Accepted 2 November 2011

Academic Editor: Ben T. Nohara

Copyright © 2012 Sohel Rana et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.