Large Deviations for Minimum Hellinger Distance Estimators

• 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): Jeffrey F. Collamore*+ and Anand Vidyashankar
• Companies: University of Copenhagen and George Mason University

Abstract

Minimum Hellinger Distance Estimators (MHDE) have long been studied, with various improvements and modifications culminating in the minimum disparity theory of estimation. Recently, this work has been extended to Bayesian inference, nonlinear regression, and high-dimensional problems. This talk will focus on exponential upper bounds for MHDE and develop sharp concentration inequalities. As a consequence of our work, we establish a large deviation principle for MHDE and, more generally, for minimum disparity estimators. We use these results to describe finite sample inference for minimum distance based methods. Tradeoff between robustness and efficiency via large deviations will also be described.