Bernstein Von Mises Theorem for linear functionals of the density

2009/08/28 by Vincent Rivoirard, Judith Rousseau, Rivoirard, Vincent +1 · 3 citations
Mathematics · #62F15 #62G20 #FOS: Mathematics #Statistics Theory (math.ST) #math.ST #msc:62F15 #msc:62G20 #stat.TH

paper · pdf · doi:10.48550/arxiv.0908.4167

36 pages

arxiv created 2009/08/28 · arxiv updated 2009/12/01

Abstract

In this paper, we study the asymptotic posterior distribution of linear functionals of the density. In particular, we give general conditions to obtain a semiparametric version of the Bernstein-Von Mises theorem. We then apply this general result to nonparametric priors based on infinite dimensional exponential families. As a byproduct, we also derive adaptive nonparametric rates of concentration of the posterior distributions under these families of priors on the class of Sobolev and Besov spaces.

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