Bayesian Optimal Adaptive Estimation Using a Sieve prior
AbstractWe derive rates of contraction of posterior distributions on nonparametric models resulting from sieve priors. The aim of the paper is to provide general conditions to get posterior rates when the parameter space has a general structure, and rate adaptation when the parameter space is, e.g., a Sobolev class. The conditions employed, although standard in the literature, are combined in a different way. The results are applied to density, regression, nonlinear autoregression and Gaussian white noise models. In the latter we have also considered a loss function which is different from the usual l2 norm, namely the pointwise loss. In this case it is possible to prove that the adaptive Bayesian approach for the l2 loss is strongly suboptimal and we provide a lower bound on the rate.
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Bibliographic InfoPaper provided by Centre de Recherche en Economie et Statistique in its series Working Papers with number 2013-19.
Date of creation: Dec 2013
Date of revision:
adaptation; minimax criteria; nonparametric models; rate of contraction; sieve prior; white noise model;
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