Density estimation for mixed Euclidean and non-Euclidean data in the presence of measurement error

In this paper, we study density estimation for mixed Euclidean and non-Euclidean variables that are subject to measurement errors. This problem is largely unexplored in statistics. We develop a new deconvolution density estimator and derive its finite-sample properties. We also derive its asymptotic...

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Bibliographic Details
Published inJournal of multivariate analysis Vol. 193; p. 105125
Main Authors Jeon, Jeong Min, Van Keilegom, Ingrid
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.01.2023
Subjects
Density estimation
Measurement error
Non-Euclidean data
secondary
Density estimation
Non-Euclidean data
Measurement error
primary
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Summary:In this paper, we study density estimation for mixed Euclidean and non-Euclidean variables that are subject to measurement errors. This problem is largely unexplored in statistics. We develop a new deconvolution density estimator and derive its finite-sample properties. We also derive its asymptotic properties including the rate of convergence in various modes and the asymptotic distribution. For the derivation, we apply Fourier analysis on topological groups, which has not been well used in statistics. We provide full practical details on the implementation of the estimator as well as several simulation studies and real data analysis.
ISSN:0047-259X
1095-7243
DOI:10.1016/j.jmva.2022.105125