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- W3121614405 abstract "In this paper, we investigate the asymptotic properties of nonparametric Bayesian mixtures of Betas for estimating a smooth density on [0, 1]. We consider a parametrization of Beta distributions in terms of mean and scale parameters and construct a mixture of these Betas in the mean parameter, while putting a prior on this scaling parameter. We prove that such Bayesian nonparametric models have good frequentist asymptotic properties. We determine the posterior rate of concentration around the true density and prove that it is the minimax rate of concentration when the true density belongs to a Holder class with regularity β, for all positive β, leading to a minimax adaptive estimating procedure of the density. We also believe that the approximating results obtained on these mixtures of Beta densities can be of interest in a frequentist framework." @default.
- W3121614405 created "2021-02-01" @default.
- W3121614405 creator A5079569621 @default.
- W3121614405 date "2010-01-01" @default.
- W3121614405 modified "2023-09-27" @default.
- W3121614405 title "Rates of convergence for the posterior distributions of mixtures of Betas and adaptive nonparametric estimation of the density" @default.
- W3121614405 hasPublicationYear "2010" @default.
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