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

Abstract Details

Activity Number: 24
Type: Topic Contributed
Date/Time: Sunday, August 1, 2010 : 2:00 PM to 3:50 PM
Sponsor: IMS
Abstract - #306802
Title: Nonlinear Regression and Bayesian Robustness via Disparities
Author(s): Giles Hooker*+
Companies: Cornell University
Address: 1186 Comstock Hall, Ithaca, NY, 14853, USA
Keywords: disparity ; robust inference ; nonlinear regression ; Hellinger distance ; kernel density ; MCMC
Abstract:

Disparity based inference proceeds by minimizing a measure of disparity between a parametric family of density functions and a kernel density estimate based on observed i.i.d. data. For a class of disparity measures, of which Hellinger distance is one of the best known, minimum disparity estimates of parameters are both robust to outliers and also statistically efficient.

This talk introduces three novel methods based on disparities. We develop two disparity-based approaches for nonlinear regression settings, based either on a non-parametric estimate of a conditional density, or by considering the marginal distribution of residuals. Both approaches can be shown to be both robust and efficient. We also demonstrate that disparities can be used to replace log likelihoods in Bayesian inference, allowing Monte Carlo Markov Chain methods to be applied to obtain robust posterior distributions


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