Abstract
The common unknown probability law $P$ of a random sample $Y_1,\ldots, Y_n$ is assigned a Dirichlet process prior with index $\alpha$. It is shown that the posterior joint density of several moments of $P$ converges, as $\alpha(\mathbb{R})\rightarrow 0$, 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.
Citation
Mauro Gasparini. "Exact Multivariate Bayesian Bootstrap Distributions of Moments." Ann. Statist. 23 (3) 762 - 768, June, 1995. https://doi.org/10.1214/aos/1176324620
Information