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

Handle URI:
http://hdl.handle.net/10754/597657
Title:
Bayesian Semiparametric Density Deconvolution in the Presence of Conditionally Heteroscedastic Measurement Errors
Authors:
Sarkar, Abhra; Mallick, Bani K.; Staudenmayer, John; Pati, Debdeep; Carroll, Raymond J.
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 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, 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. 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 data set and R programs implementing our methods are included as part of online supplemental materials.
Citation:
Sarkar A, Mallick BK, Staudenmayer J, Pati D, Carroll RJ (2014) Bayesian Semiparametric Density Deconvolution in the Presence of Conditionally Heteroscedastic Measurement Errors. Journal of Computational and Graphical Statistics 23: 1101–1125. Available: http://dx.doi.org/10.1080/10618600.2014.899237.
Publisher:
Informa UK Limited
Journal:
Journal of Computational and Graphical Statistics
KAUST Grant Number:
KUS-CI-016-04
Issue Date:
2-Oct-2014
DOI:
10.1080/10618600.2014.899237
PubMed ID:
25378893
PubMed Central ID:
PMC4219602
Type:
Article
ISSN:
1061-8600; 1537-2715
Sponsors:
Carroll's research was supported in part by grants R37-CA057030 and R25T-CA090301 from the National Cancer Institute. Mallick's research was supported in part by National Science Foundation grant DMS0914951. Staudenmayer's work was supported in part by NIH grants CA121005 and R01-HL099557. The authors thank Jeff Hart, John P. Buonaccorsi, and Susanne M. Schennach for their helpful suggestions. The authors also acknowledge the Texas A&M University Brazos HPC cluster that contributed to the research reported here. This publication is based in part on work supported by Award Number KUS-CI-016-04, made by King Abdullah University of Science and Technology (KAUST).
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Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorSarkar, Abhraen
dc.contributor.authorMallick, Bani K.en
dc.contributor.authorStaudenmayer, Johnen
dc.contributor.authorPati, Debdeepen
dc.contributor.authorCarroll, Raymond J.en
dc.date.accessioned2016-02-25T12:43:51Zen
dc.date.available2016-02-25T12:43:51Zen
dc.date.issued2014-10-02en
dc.identifier.citationSarkar A, Mallick BK, Staudenmayer J, Pati D, Carroll RJ (2014) Bayesian Semiparametric Density Deconvolution in the Presence of Conditionally Heteroscedastic Measurement Errors. Journal of Computational and Graphical Statistics 23: 1101–1125. Available: http://dx.doi.org/10.1080/10618600.2014.899237.en
dc.identifier.issn1061-8600en
dc.identifier.issn1537-2715en
dc.identifier.pmid25378893en
dc.identifier.doi10.1080/10618600.2014.899237en
dc.identifier.urihttp://hdl.handle.net/10754/597657en
dc.description.abstractWe 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, 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. 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 data set and R programs implementing our methods are included as part of online supplemental materials.en
dc.description.sponsorshipCarroll's research was supported in part by grants R37-CA057030 and R25T-CA090301 from the National Cancer Institute. Mallick's research was supported in part by National Science Foundation grant DMS0914951. Staudenmayer's work was supported in part by NIH grants CA121005 and R01-HL099557. The authors thank Jeff Hart, John P. Buonaccorsi, and Susanne M. Schennach for their helpful suggestions. The authors also acknowledge the Texas A&M University Brazos HPC cluster that contributed to the research reported here. This publication is based in part on work supported by Award Number KUS-CI-016-04, made by King Abdullah University of Science and Technology (KAUST).en
dc.publisherInforma UK Limiteden
dc.subjectMeasurement Errorsen
dc.subjectB-splineen
dc.subjectSkew-normal Distributionen
dc.subjectVariance Functionen
dc.subjectConditional Heteroscedasticityen
dc.subjectDirichlet Process Mixture Modelsen
dc.subjectDensity Deconvolutionen
dc.titleBayesian Semiparametric Density Deconvolution in the Presence of Conditionally Heteroscedastic Measurement Errorsen
dc.typeArticleen
dc.identifier.journalJournal of Computational and Graphical Statisticsen
dc.identifier.pmcidPMC4219602en
dc.contributor.institutionDepartment of Statistics, Texas A&M University, 3143 TAMU, College Station, TX 77843-3143 USA.en
dc.contributor.institutionDepartment of Mathematics and Statistics, University of Massachusetts, Amherst, MA 01003-9305 USA.en
dc.contributor.institutionDepartment of Statistics, Florida State University, Tallahassee, FL 32306-4330 USA.en
kaust.grant.numberKUS-CI-016-04en
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