This is the program for the 2010 Joint Statistical Meetings in Vancouver, British Columbia.

Abstract Details

Activity Number: 122
Type: Topic Contributed
Date/Time: Monday, August 2, 2010 : 8:30 AM to 10:20 AM
Sponsor: Section on Nonparametric Statistics
Abstract - #306899
Title: Predictive Recursion: Convergence Theory, Extensions, and Applications
Author(s): Ryan Martin*+ and Surya Tokdar
Companies: Indiana University Purdue University Indianapolis and Duke University
Address: 402 N. Blackford St., Indianapolis, IN, 46202,
Keywords: nonparametrics ; mixture model ; empirical Bayes ; semiparametrics ; stochastic approximation ; density estimation

Predictive Recursion (PR) is a fast, recursive algorithm designed for nonparametric estimation of mixing distributions. I will present some new theory that describes the asymptotic behavior of PR estimates of the mixing distribution and mixture density under model mis-specification. In particular, the PR estimate of the mixture density converges almost surely in the total variation topology to the mixture which is closest, in a Kullback-Leibler sense, to the true data-generating density. Under extra conditions, results on the (minimax) rate of convergence as well as weak convergence of the PR estimate of the mixing distribution are available. The new asymptotic robustness results lead to an attractive construction of a semiparametric version of PR; details of this new algorithm will be given, along with some basic convergence theory. Empirical Bayes applications will be considered.

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