Bayesian Semiparametric Multivariate Density Deconvolution
成果类型：
Article
署名作者：
Sarkar, Abhra; Pati, Debdeep; Chakraborty, Antik; Mallick, Bani K.; Carroll, Raymond J.
署名单位：
Duke University; University of Texas System; University of Texas Austin; State University System of Florida; Florida State University; Texas A&M University System; Texas A&M University College Station; University of Technology Sydney
刊物名称：
JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
ISSN/ISSBN：
0162-1459
DOI：
10.1080/01621459.2016.1260467
发表日期：
2018
页码：
401-416
关键词：
nonparametric deconvolution
Optimal Rates
CONVERGENCE
regression
inference
models
摘要：
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.