Abstract:
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Recently, several authors studying the asymptotic performance of nonparametric Bayesian models for density estimation have succeeded in establishing fast posterior contraction rates that mimic frequentist rates, yet most of these authors' results require the true density to have exponentially decaying tails or compact support. In this paper we show that by incorporating a tail-correcting transformation of the sample and modeling the transformed density using a Dirichlet process mixture, the same fast rates can be obtained for a much broader class of densities, including those with polynomially decaying tails. Empirical evidence is given for the effectiveness of the transformation method, including an analysis of a heavy-tailed sample of body mass index (BMI) observations for a large survey of Ohio adults.
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