Robust Winsorized Regression Using Bootstrap Approach

Abstract

The history of regression analysis when response and explanatory variables are subject to error dates back to Eisenhart (1939) and Wald (1940). Now the subject is discussed in the robust regression framework involving “leverage” points in addition to the traditional “outliers,” e.g., see Rousseeuw and Leroy (1987). In this article, we develop two variations of co-ordinatewise Winsorized-bootstrapped approach and study their properties using empirical methods and illustrative examples. The new methods are seen to provide significant improvement when the data are in a neighborhood of multivariate normal population without significant loss in the performance when the multivariate normal model holds.

Keywords:

• Bootstrap
• Linear regression
• Robustness
• Winsorization

Mathematics Subject Classification:

• 62G09
• 62F35
• 62F40
• 62J05

Acknowledgments

The research work of Deo Kumar Srivastava and Jianmin Pan was in part supported by the Grant CA21765 and the American Lebanese Syrian Associated Charities. The authors are thankful to the referees for their constructive comments and suggestions.

Notes

*For details regarding parameter selection see Sec.

*See Sec. for explanation.