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Asymptotic properties of posterior distributions in nonparametric regression with non-Gaussian errors

Authors
Choi, Taeryon
Issue Date
Dec-2009
Publisher
SPRINGER HEIDELBERG
Keywords
Posterior consistency; Uniformly consistent tests; Kullback-Leibler divergence; Hellinger metric; Prior positivity; Symmetric density
Citation
ANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICS, v.61, no.4, pp 835 - 859
Pages
25
Indexed
SCIE
SCOPUS
Journal Title
ANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICS
Volume
61
Number
4
Start Page
835
End Page
859
URI
https://scholar.korea.ac.kr/handle/2021.sw.korea/118884
DOI
10.1007/s10463-008-0168-2
ISSN
0020-3157
1572-9052
Abstract
We investigate the asymptotic behavior of posterior distributions in nonparametric regression problems when the distribution of noise structure of the regression model is assumed to be non-Gaussian but symmetric such as the Laplace distribution. Given prior distributions for the unknown regression function and the scale parameter of noise distribution, we show that the posterior distribution concentrates around the true values of parameters. Following the approach by Choi and Schervish (Journal of Multivariate Analysis, 98, 1969-1987, 2007) and extending their results, we prove consistency of the posterior distribution of the parameters for the nonparametric regression when errors are symmetric non-Gaussian with suitable assumptions.
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