A Bernstein-von Mises theorem for smooth functionals in semiparametric models
Abstract
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 -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.
Cite
@article{arxiv.1305.4482,
title = {A Bernstein-von Mises theorem for smooth functionals in semiparametric models},
author = {Ismaël Castillo and Judith Rousseau},
journal= {arXiv preprint arXiv:1305.4482},
year = {2016}
}
Comments
Published at http://dx.doi.org/10.1214/15-AOS1336 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)