Bayesian Optimal Adaptive Estimation Using a Sieve prior
We 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.
|Date of creation:||Dec 2013|
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- Rousseau, Judith & Chopin, Nicolas & Liseo, Brunero, 2012.
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Economics Papers from University Paris Dauphine
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- Judith Rousseau & Nicolas Chopin & Brunero Liseo, 2010. "Bayesian Nonparametric Estimation of the Spectral Density of a Long or Intermediate Memory Gaussian Process," Working Papers 2010-38, Centre de Recherche en Economie et Statistique.
- Rousseau, Judith, 2010. "Rates of convergence for the posterior distributions of mixtures of Betas and adaptive nonparametric estimation of the density," Economics Papers from University Paris Dauphine 123456789/3984, Paris Dauphine University.
- Felix Abramovich & Claudia Angelini & Daniela Canditiis, 2007. "Pointwise optimality of Bayesian wavelet estimators," Annals of the Institute of Statistical Mathematics, Springer, vol. 59(3), pages 425-434, September.
- Rivoirard, Vincent & Rousseau, Judith, 2012. "Posterior concentration rates for infinite dimensional exponential families," Economics Papers from University Paris Dauphine 123456789/7335, Paris Dauphine University.
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