## 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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