Measures of Robustness in Regularized Estimates

• Activity Number: 161
• Type: Topic Contributed
• Date/Time: Monday, August 5, 2013 : 10:30 AM to 12:20 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Giles Hooker*+
• Companies: Cornell University
• Keywords: Disparity ; Robustness ; Breakdown Point ; Shrinkage ; Regularization ; Penalty

Abstract

This talk examines the use of measures of robustness as applied to shrinkage methods and other regularized estimators. When penalization or shrinkage is applied to robust M-estimators, common measures of robustness such as influence functions and breakdown points can prove misleading. Specifically, many such estimators have breakdown points of one which does not distinguish them from trivially-robust estimators such as those based on thresholding non-robust estimators. Instead, we propose measures based on asymptotic performance that are able to make this distinction. These ideas are demonstrate via methods that incorporate disparity estimates into Bayesian inference and we discuss the relationship of these measures with Bayesian notion of "outlier rejection" in heavy-tailed models.