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Activity Number: 4
Type: Invited
Date/Time: Sunday, August 4, 2013 : 2:00 PM to 3:50 PM
Sponsor: IMS
Abstract - #307366
Title: Bayesian Semiparametric Density Deconvolution in the Presence of Conditionally Heteroscedastic Measurement Errors
Author(s): Raymond J. Carroll and Abhra Sarkar and Bani Mallick and John Staudenmayer*+ and Debdeep Pati
Companies: Texas A&M University and Texas A&M University and Texas A&M and University of Massachusetts and Florida State University
Keywords: B-spline ; Density deconvolution ; Heteroscedasticity ; Variancd function estimation ; Dirichlet process mixture models
Abstract:

We consider the problem of estimating the density of a random variable when precise measurements on the variable are not available, but replicated proxies contaminated with measurement error are available for each subject. Under the assumption of additive measurement errors this reduces to a problem of deconvolution of densities. Deconvolution methods often make restrictive and unrealistic assumptions about the density of interest and the distribution of measurement errors, e.g., normality and homoscedasticity and thus independence from the variable of interest. This article relaxes these assumptions and introduces novel Bayesian semiparametric methodology based on Dirichlet process mixture models for robust deconvolution of densities in the presence of conditionally heteroscedastic measurement errors. We show theoretically the flexibility of the proposed models, and in particular that the models can adapt to asymmetry, heavy tails and multimodality. In simulation experiments, we show that our methods vastly outperform a recent Bayesian approach based on estimating the densities via mixtures of splines, and this improvement even occurs with normally distributed measurement errors


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