University of Washington - Department of Statistics
This talk will begin with a brief historical overview of what I consider to be the main concepts and classes of estimators. The main robustness concepts, based on contamination (mixture) models for the data are efficiency robustness, high-breakdown point, and bias robustness. The main estimators are M-estimators, bounded-influence estimators, and least-median-of-squares (LMS) and least-trimmed squares (LTS) estimators. The strengths and weaknesses of the various estimators are described, and we will emphasize a particular M-estimator due to Yohai and Zamar (1997). This modern robust regression estimate has a highly desirable theoretical justification in terms of Gaussian model efficiency and maximum bias control under contamination models. The Yohai and Zamar estimator was implemented in S-PLUS 4.5 in 1998. I will comment on why robust estimators have not come into mainstream use to date, and a strategy initiated in the S-PLUS 4.5 implementation for bringing robust regression (and other robust modeling) methods into mainstream use. Three striking applications of robust straight line fitting in finance will be provided: estimating beta, modeling the relationship between a firm's returns and size, and estimating an optimal hedge ratio. Other potential applications in finance are briefly mentioned. Finally, a few important open issues are discussed.