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

Sarkar, A; Mallick, BK; Staudenmayer, J; Pati, D; Carroll, RJ

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

Sarkar, A Mallick, BK Staudenmayer, J Pati, D Carroll, RJ

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Publication Type:: Journal Article
Citation:: Journal of Computational and Graphical Statistics, 2014, 23 (4), pp. 1101 - 1125
Issue Date:: 2014-01-01

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Field	Value	Language
dc.contributor.author	Sarkar, A	en_US
dc.contributor.author	Mallick, BK	en_US
dc.contributor.author	Staudenmayer, J	en_US
dc.contributor.author	Pati, D	en_US
dc.contributor.author	Carroll, RJ https://orcid.org/0000-0002-5465-9682	en_US
dc.date.issued	2014-01-01	en_US
dc.identifier.citation	Journal of Computational and Graphical Statistics, 2014, 23 (4), pp. 1101 - 1125	en_US
dc.identifier.issn	1061-8600	en_US
dc.identifier.uri	http://hdl.handle.net/10453/117867
dc.description.abstract	© 2014, © 2014 American Statistical Association, Institute of Mathematical Statistics, and Interface Foundation of North America. 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 sufficiently many subjects. 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, for example, 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. In particular, 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. We apply our methods to data from nutritional epidemiology. Even in the special case when the measurement errors are homoscedastic, our methodology is novel and dominates other methods that have been proposed previously. Additional simulation results, instructions on getting access to the dataset and R programs implementing our methods are included as part of online supplementary materials.	en_US
dc.relation.ispartof	Journal of Computational and Graphical Statistics	en_US
dc.relation.isbasedon	10.1080/10618600.2014.899237	en_US
dc.subject.classification	Statistics & Probability	en_US
dc.title	Bayesian Semiparametric Density Deconvolution in the Presence of Conditionally Heteroscedastic Measurement Errors	en_US
dc.type	Journal Article
utslib.citation.volume	4	en_US
utslib.citation.volume	23	en_US
utslib.for	0104 Statistics	en_US
utslib.for	1403 Econometrics	en_US
pubs.embargo.period	Not known	en_US
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Science
pubs.organisational-group	/University of Technology Sydney/Faculty of Science/School of Mathematical and Physical Sciences
utslib.copyright.status	closed_access
pubs.issue	4	en_US
pubs.publication-status	Published	en_US
pubs.volume	23	en_US

Abstract:

© 2014, © 2014 American Statistical Association, Institute of Mathematical Statistics, and Interface Foundation of North America. 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 sufficiently many subjects. 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, for example, 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. In particular, 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. We apply our methods to data from nutritional epidemiology. Even in the special case when the measurement errors are homoscedastic, our methodology is novel and dominates other methods that have been proposed previously. Additional simulation results, instructions on getting access to the dataset and R programs implementing our methods are included as part of online supplementary materials.

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http://hdl.handle.net/10453/117867