Bayesian Semiparametric Density Deconvolution in the Presence of Conditionally Heteroscedastic Measurement Errors

• Activity Number: 297
• Type: Topic Contributed
• Date/Time: Tuesday, August 6, 2013 : 8:30 AM to 10:20 AM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Abhra Sarkar*+ and Bani Mallick and John Staudenmayer and Debdeep Pati and Raymond J. Carroll
• Companies: Texas A&M University and Texas A&M and University of Massachusetts and Florida State University and Texas A&M University
• Keywords: B-spline ; Conditional heteroscedasticity ; Density deconvolution ; Measurement errors ; Skew-normal distribution ; Variance Function

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 independence from the variable of interest. This article relaxes these assumptions and introduces novel Bayesian semiparametric methodology for robust deconvolution of densities in the presence of conditionally heteroscedastic measurement errors. We show theoretically the flexibility of the proposed models. 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. We apply our methods to data from nutritional epidemiology.