Robustness of Estimators of Location to Distortion

• Activity Number: 188
• Type: Contributed
• Date/Time: Monday, August 2, 2010 : 10:30 AM to 12:20 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Demetris Athientis*+ and Ronald Randles
• Companies: University of Florida and University of Florida
• Keywords: Robust ; Asymmetry ; Skewness ; Location

Abstract

Robustness measures and procedures have traditionally been developed and implemented through the contamination model; a model that partially samples from a contaminant distribution. Hampel (1968), developed a heuristic tool, the influence function, that represents the rate of change in a statistic by adding an infinitesimal amount of contamination. We present a distortion model that takes a symmetric probability density function and skews it in a specific direction thereby distorting every realization of the distribution. The model used is based upon the Fechner class of distributions first introduced by Fechner (1897). A plethora of statistical procedures assume distributional symmetry and we set out to derive various robustness properties for the distortion model, of which symmetry is only a special case, by introducing the distortion sensitivity.