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Bayesian semiparametric multivariate density deconvolution via stochastic rotation of replicates

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  • Roy, Arkaprava
  • Sarkar, Abhra

Abstract

In multivariate density deconvolution, the distribution of a random vector needs to be estimated from replicates contaminated with measurement errors. A novel approach to multivariate deconvolution is proposed by stochastically rotating and stretching or contracting the replicates toward the corresponding true latent values. The method further accommodates conditionally heteroscedastic measurement errors commonly observed in many real data applications. The estimation and inference schemes are developed within a Bayesian framework implemented via an efficient Markov chain Monte Carlo algorithm, appropriately accommodating uncertainty in all aspects of the analysis. The method's efficacy is demonstrated empirically through simulation experiments and practically in estimating the long-term joint average intakes of different dietary components from their measurement error-contaminated 24-hour dietary recalls.

Suggested Citation

  • Roy, Arkaprava & Sarkar, Abhra, 2023. "Bayesian semiparametric multivariate density deconvolution via stochastic rotation of replicates," Computational Statistics & Data Analysis, Elsevier, vol. 182(C).
    • Handle: RePEc:eee:csdana:v:182:y:2023:i:c:s0167947323000178
    DOI: 10.1016/j.csda.2023.107706
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    References listed on IDEAS

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    1. Abhra Sarkar & Debdeep Pati & Antik Chakraborty & Bani K. Mallick & Raymond J. Carroll, 2018. "Bayesian Semiparametric Multivariate Density Deconvolution," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(521), pages 401-416, January.
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    6. Élie Youndjé & Martin Wells, 2008. "Optimal bandwidth selection for multivariate kernel deconvolution density estimation," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 17(1), pages 138-162, May.
    7. Li, Tong & Vuong, Quang, 1998. "Nonparametric Estimation of the Measurement Error Model Using Multiple Indicators," Journal of Multivariate Analysis, Elsevier, vol. 65(2), pages 139-165, May.
    8. Abhra Sarkar & Debdeep Pati & Bani K. Mallick & Raymond J. Carroll, 2021. "Bayesian Copula Density Deconvolution for Zero-Inflated Data in Nutritional Epidemiology," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 116(535), pages 1075-1087, July.
    9. Staudenmayer, John & Ruppert, David & Buonaccorsi, John P., 2008. "Density Estimation in the Presence of Heteroscedastic Measurement Error," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 726-736, June.
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