## The Annals of Statistics

### Exact Multivariate Bayesian Bootstrap Distributions of Moments

Mauro Gasparini

#### 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.

#### Article information

Source
Ann. Statist., Volume 23, Number 3 (1995), 762-768.

Dates
First available in Project Euclid: 11 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176324620

Digital Object Identifier
doi:10.1214/aos/1176324620

Mathematical Reviews number (MathSciNet)
MR1345198

Zentralblatt MATH identifier
0838.62032

JSTOR