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A Bernstein-von Mises theorem for smooth functionals in semiparametric models

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1305.4482.pdf (333.0Kb)
Date
2015
Dewey
Probabilités et mathématiques appliquées
Sujet
Bayesian nonparametrics; Bernstein–von Mises theorem; posterior concentration; semiparametric inference
Journal issue
The Annals of Statistics
Volume
43
Number
6
Publication date
10-2015
Article pages
2353-2383
DOI
http://dx.doi.org/10.1214/15-AOS1336
URI
https://basepub.dauphine.fr/handle/123456789/17291
Collections
  • CEREMADE : Publications
Metadata
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Author
Castillo, Ismaël
102 Laboratoire de Probabilités et Modèles Aléatoires [LPMA]
Rousseau, Judith
60 CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
2579 Centre de Recherche en Économie et Statistique [CREST]
Type
Article accepté pour publication ou publié
Abstract (EN)
A Bernstein–von Mises theorem is derived for general semiparametric functionals. The result is applied to a variety of semiparametric problems in i.i.d. and non-i.i.d. situations. In particular, new tools are developed to handle semiparametric bias, in particular for nonlinear functionals and in cases where regularity is possibly low. Examples include the squared L2-norm in Gaussian white noise, nonlinear functionals in density estimation, as well as functionals in autoregressive models. For density estimation, a systematic study of BvM results for two important classes of priors is provided, namely random histograms and Gaussian process priors.

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