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December 2015 A Bernstein–von Mises theorem for smooth functionals in semiparametric models
Ismaël Castillo, Judith Rousseau
Ann. Statist. 43(6): 2353-2383 (December 2015). DOI: 10.1214/15-AOS1336


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 $L^{2}$-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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Ismaël Castillo. Judith Rousseau. "A Bernstein–von Mises theorem for smooth functionals in semiparametric models." Ann. Statist. 43 (6) 2353 - 2383, December 2015.


Received: 1 May 2013; Revised: 1 April 2015; Published: December 2015
First available in Project Euclid: 7 October 2015

zbMATH: 1327.62302
MathSciNet: MR3405597
Digital Object Identifier: 10.1214/15-AOS1336

Primary: 62G20
Secondary: 62M15

Keywords: Bayesian nonparametrics , Bernstein–von Mises theorem , posterior concentration , semiparametric inference

Rights: Copyright © 2015 Institute of Mathematical Statistics


Vol.43 • No. 6 • December 2015
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