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

Castillo, Ismaël; Rousseau, Judith (2015), A Bernstein-von Mises theorem for smooth functionals in semiparametric models, The Annals of Statistics, 43, 6, p. 2353-2383. 10.1214/15-AOS1336

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Type
Article accepté pour publication ou publié
Date
2015
Journal name
The Annals of Statistics
Volume
43
Number
6
Pages
2353-2383
Publication identifier
Metadata
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Author(s)
Castillo, Ismaël
Laboratoire de Probabilités et Modèles Aléatoires [LPMA]
Rousseau, Judith
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Centre de Recherche en Économie et Statistique [CREST]
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.
Subjects / Keywords
Bayesian nonparametrics; Bernstein–von Mises theorem; posterior concentration; semiparametric inference