Bivariate Kernel Deconvolution with Panel Data

Guillermo Basulto-Elias (), Alicia L. Carriquiry, Kris Brabanter and Daniel J. Nordman
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Guillermo Basulto-Elias: Iowa State University
Alicia L. Carriquiry: Iowa State University
Kris Brabanter: Iowa State University
Daniel J. Nordman: Iowa State University

Sankhya B: The Indian Journal of Statistics, 2021, vol. 83, issue 1, No 6, 122-151

Abstract: Abstract We consider estimation of the density of a multivariate response, that is not observed directly but only through measurements contaminated by additive error. Our focus is on the realistic sampling case of bivariate panel data (repeated contaminated bivariate measurements on each sample unit) with an unknown error distribution. Several factors can affect the performance of kernel deconvolution density estimators, including the choice of the kernel and the estimation approach of the unknown error distribution. As the choice of the kernel function is critically important, the class of flat-top kernels can have advantages over more commonly implemented alternatives. We describe different approaches for density estimation with multivariate panel responses, and investigate their performance through simulation. We examine competing kernel functions and describe a flat-top kernel that has not been used in deconvolution problems. Moreover, we study several nonparametric options for estimating the unknown error distribution. Finally, we also provide guidelines to the numerical implementation of kernel deconvolution in higher sampling dimensions.

Keywords: Deconvolution density estimation; empirical characteristic function; flat-top kernel; measurement error.; Primary 62G07; Secondary 65T50 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s13571-020-00226-x

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