Bayesian Semiparametric Multivariate Density Deconvolution. Issue 521 (2nd January 2018)

• Record Type: Journal Article
• Authors: Sarkar, Abhra; Pati, Debdeep; Chakraborty, Antik; Mallick, Bani K.; Carroll, Raymond J.
• Is Part Of: Journal of the American Statistical Association. Volume 113:Issue 521(2018)
• Page Start: 401
• Page End: 416
• Publication Date: 2018-01-02
• Subjects: B-splines -- Conditional heteroscedasticity -- Latent factor analyzers -- Measurement errors -- Mixture models -- Multivariate density deconvolution -- Regularization -- Shrinkage; Statistics -- Periodicals; Statistics -- Periodicals; Statistiques -- Périodiques; États-Unis -- Statistiques -- Périodiques; 519.5
• DOI: 10.1080/01621459.2016.1260467
• Languages: English
• ISSNs: 0162-1459

Abstract

ABSTRACT: We consider the problem of multivariate density deconvolution when interest lies in estimating the distribution of a vector valued random variable X but precise measurements on X are not available, observations being contaminated by measurement errors U . The existing sparse literature on the problem assumes the density of the measurement errors to be completely known. We propose robust Bayesian semiparametric multivariate deconvolution approaches when the measurement error density of U is not known but replicated proxies are available for at least some individuals. Additionally, we allow the variability of U to depend on the associated unobserved values of X through unknown relationships, which also automatically includes the case of multivariate multiplicative measurement errors. Basic properties of finite mixture models, multivariate normal kernels, and exchangeable priors are exploited in novel ways to meet modeling and computational challenges. Theoretical results showing the flexibility of the proposed methods in capturing a wide variety of data-generating processes are provided. We illustrate the efficiency of the proposed methods in recovering the density of X through simulation experiments. The methodology is applied to estimate the joint consumption pattern of different dietary components from contaminated 24 h recalls. Supplementary materials for this article are available online.