Bernstein Von Mises Theorem for linear functionals of the density - Mathematics > Statistics TheoryReport as inadecuate




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Abstract: In this paper, we study the asymptotic posterior distribution of linearfunctionals of the density. In particular, we give general conditions to obtaina semiparametric version of the Bernstein-Von Mises theorem. We then apply thisgeneral result to nonparametric priors based on infinite dimensionalexponential families. As a byproduct, we also derive adaptive nonparametricrates of concentration of the posterior distributions under these families ofpriors on the class of Sobolev and Besov spaces.



Author: Vincent Rivoirard, Judith Rousseau

Source: https://arxiv.org/



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