Bayesian Semiparametric Multivariate Density Deconvolution

Sarkar, Abhra; Pati, Debdeep; Chakraborty, Antik; Mallick, Bani K.; Carroll, Raymond J.

doi:10.1080/01621459.2016.1260467

Cited by 21 publications

(36 citation statements)

References 35 publications

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“…Recent references for density estimation are e.g. Comte and Lacour (2013) using kernel density estimators and Sarkar et al (2015) for a Bayesian approach in the case of an unknown error distribution with replicated proxies available. Hypothesis testing in deconvolution is investigated in Holzmann et al (2007) and Bissantz and Holzmann (2008).…”

Section: Introductionmentioning

confidence: 99%

Multiscale inference for multivariate deconvolution

Eckle¹,

Bissantz²,

Dette³

2017

Electron. J. Statist.

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In this paper we provide new methodology for inference of the geometric features of a multivariate density in deconvolution. Our approach is based on multiscale tests to detect significant directional derivatives of the unknown density at arbitrary points in arbitrary directions. The multiscale method is used to identify regions of monotonicity and to construct a general procedure for the detection of modes of the multivariate density. Moreover, as an important application a significance test for the presence of a local maximum at a pre-specified point is proposed. The performance of the new methods is investigated from a theoretical point of view and the finite sample properties are illustrated by means of a small simulation study.

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Section: Introductionmentioning

confidence: 99%

Multiscale inference for multivariate deconvolution

Eckle¹,

Bissantz²,

Dette³

2017

Electron. J. Statist.

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“…We thus need to model the joint distribution of (ξ, U i ) flexibly. To do this, we follow the flexible semiparametric approach of Sarkar et al (2017), see also Sarkar et al…”

Section: Clustering Of Relative Dietary Amountsmentioning

confidence: 99%

“…Sarkar et al (2017) do the multivariate deconvolution using an MCMC approach. In our example, we took a burn in of 1000 steps, and then generated a further sample with 4000 steps.…”

Section: Clustering Of Relative Dietary Amountsmentioning

confidence: 99%

“…In practice what we do is to regress the mean recalls W i· of the dietary variables on the covariates, obtain an estimate A, form the residuals, and then fit the model of Sarkar et al (2017) to the residuals: computation of the last step was done via an R program included in their Supplementary Material. Sarkar et al (2017) do the multivariate deconvolution using an MCMC approach.…”

Section: Clustering Of Relative Dietary Amountsmentioning

confidence: 99%

“…Computation was done using their R program. In the model of Sarkar et al (2017), the distribution of ξ was modelled by a flexible multivariate mixture of normals. Then the measurement error distribution of U i was modeled as conditionally heteroscedastic, so that…”

Section: Clustering Of Relative Dietary Amountsmentioning

confidence: 99%

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Clustering in General Measurement Error Models

Su¹,

Reedy²,

Carroll³

2018

STAT SINICA

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This paper is dedicated to the memory of Peter G. Hall. It concerns a deceptively simple question: if one observes variables corrupted with measurement error of possibly very complex form, can one recreate asymptotically the clusters that would have been found had there been no measurement error? We show that the answer is yes, and that the solution is surprisingly simple and general. The method itself is to simulate, by computer, realizations with the same distribution as that of the true variables , and then to apply clustering to these realizations. Technically, we show that if one uses K-means clustering or any other risk minimizing clustering, and a multivariate deconvolution device with certain smoothness and convergence properties, then, in the limit, the cluster means based on our method converge to the same cluster means as if there is no measurement error. Along with the method and its technical justification, we analyze two important nutrition data sets, finding patterns that make sense nutritionally.Some Key Words: Clustering; Deconvolution; K-means; Measurement error; Mixtures of distributions. Short title: Clustering and Measurement ErrorStatistica Sinica: Newly accepted Paper (accepted version subject to English editing) Dedication to the memory of Peter G. HallThe last author, Raymond J. Carroll, was very fond of Peter and visited him many times.His facets included his brilliance, dedication, kindness, sense of humor, graciousness to young researchers, puzzle solving, madcap driving to take photos of trains, discussions about airplanes, love of cats and photographic advice. As Peter said in his Statistical Science interview (Delaigle and Wand, 2016), I always like working with Ray, because I felt I could contribute something from the problem solving side, the theoretical side, whereas he is more an applied person, ... in working with Ray we bring to the table things that don't overlap, and which complemented each other very well.In his interview, Peter also mentioned that a lot of his joint work with Raymond grew out of nutrition research, and hence this paper is an appropriate contribution to this special issue. It involves a deceptively simple question: if one observes variables corrupted with measurement error of possibly complex form, such as occurs in nutritional and radiation applications, can one recreate the clusters that would have been found had there been no measurement error? We show that the answer is yes, and that the solution is surprisingly simple and general.

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A Bayesian semi‐parametric scalar‐on‐function regression with measurement error using instrumental variables

Zoh,

Luan,

Xue

et al. 2024

Statistics in Medicine

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Wearable devices such as the ActiGraph are now commonly used in research to monitor or track physical activity. This trend corresponds with the growing need to assess the relationships between physical activity and health outcomes, such as obesity, accurately. Device‐based physical activity measures are best treated as functions when assessing their associations with scalar‐valued outcomes such as body mass index. Scalar‐on‐function regression (SoFR) is a suitable regression model in this setting. Most estimation approaches in SoFR assume that the measurement error in functional covariates is white noise. Violating this assumption can lead to underestimating model parameters. There are limited approaches to correcting measurement errors for frequentist methods and none for Bayesian methods in this area. We present a non‐parametric Bayesian measurement error‐corrected SoFR model that relaxes all the constraining assumptions often involved with these models. Our estimation relies on an instrumental variable allowing a time‐varying biasing factor, a significant departure from the current generalized method of moment (GMM) approach. Our proposed method also permits model‐based grouping of the functional covariate following measurement error correction. This grouping of the measurement error‐corrected functional covariate allows additional ease of interpretation of how the different groups differ. Our method is easy to implement, and we demonstrate its finite sample properties in extensive simulations. Finally, we applied our method to data from the National Health and Examination Survey to assess the relationship between wearable device‐based measures of physical activity and body mass index in adults in the United States.

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Bayesian Semiparametric Multivariate Density Deconvolution

Cited by 21 publications

References 35 publications

Multiscale inference for multivariate deconvolution

Multiscale inference for multivariate deconvolution

Clustering in General Measurement Error Models

A Bayesian semi‐parametric scalar‐on‐function regression with measurement error using instrumental variables

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