A BERNSTEIN-VON MISES THEOREM FOR SMOOTH FUNCTIONALS IN SEMIPARAMETRIC MODELS

• 成果类型: Article
• 署名作者: Castillo, Ismael; Rousseau, Judith
• 署名单位: Sorbonne Universite; Universite Paris Cite; Institut Polytechnique de Paris; ENSAE Paris; Universite PSL; Universite Paris-Dauphine
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/15-AOS1336
• 发表日期: 2015
• 页码: 2353-2383
• 关键词: optimal adaptive estimation; posterior distributions; Asymptotic Normality; rates; contraction

摘要

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.