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Exact multivariate Bayesian bootstrap distributions of moments. (English) Zbl 0838.62032

Summary: The common unknown probability law \(P\) of a random sample \(Y_1, \dots, Y_n\) is assigned a Dirichlet process prior with index \(\alpha\). It is shown that the posterior joint density of several moments of \(P\) converges, as \(\alpha (\mathbb{R})\to 0\), to a multivariate \(B\)-spline, which is, therefore, the Bayesian bootstrap joint density of the moments. The result provides the basis for possible default nonparametric Bayesian inference on unknown moments.

MSC:

62G09 Nonparametric statistical resampling methods
62G20 Asymptotic properties of nonparametric inference
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