NONPARAMETRIC BERNSTEIN-VON MISES THEOREMS IN GAUSSIAN WHITE NOISE

• 成果类型: Article
• 署名作者: Castillo, Ismael; Nickl, Richard
• 署名单位: Centre National de la Recherche Scientifique (CNRS); Sorbonne Universite; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); University of Cambridge
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/13-AOS1133
• 发表日期: 2013
• 页码: 1999-2028
• 关键词: posterior distributions; density estimators; exponential-families; Asymptotic Normality; convergence-rates; LIMIT-THEOREMS; priors; contraction; functionals; parameters

摘要

Bernstein-von Mises theorems for nonparametric Bayes priors in the Gaussian white noise model are proved. It is demonstrated how such results justify Bayes methods as efficient frequentist inference procedures in a variety of concrete nonparametric problems. Particularly Bayesian credible sets are constructed that have asymptotically exact 1 - alpha frequentist coverage level and whose L-2-diameter shrinks at the minimax rate of convergence (within logarithmic factors) over Holder balls. Other applications include general classes of linear and nonlinear functionals and credible bands for auto-convolutions. The assumptions cover nonconjugate product priors defined on general orthonormal bases of L-2 satisfying weak conditions.