Bayesian Density Estimates in Minimum Hellinger Distance Estimation

• Activity Number: 24
• Type: Topic Contributed
• Date/Time: Sunday, August 1, 2010 : 2:00 PM to 3:50 PM
• Sponsor: IMS
• Author(s): Yuefeng Wu*+
• Companies: Cornell University
• Keywords: minimum Hellinger distance estimation ; Bayesian density estimation ; robust ; efficiency

Abstract

This talk studies the use of Bayesian estimates of nonparametric densities in minimum Hellinger Distance estimation to obtain robust parameter estimates for i.i.d. data. We demonstrate the robustness, consistency and convergence rates of the resulting estimates in a general framework. Further, we demonstrate that the Hellinger Distance measure can be used to modify the prior for the non-parametric density, obtaining a hierarchical model. This approach unifies Bayesian density estimation and the use of Hellinger distance to obtain robust posteriors. We demonstrate that the resulting Bayesian parameter estimates retain the statistical properties of the estimates discussed above and provide MCMC methods to compute posterior distributions. The finite-sample applicability of our assymptotic analysis is verified by simulation.