The Annals of Statistics

Exact Multivariate Bayesian Bootstrap Distributions of Moments

Mauro Gasparini

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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
links.jstor.org

Subjects
Primary: 62G05: Estimation
Secondary: 62P99: None of the above, but in this section

Keywords
Dirichlet priors multivariate B-splines Bayesian bootstrap

Citation

Gasparini, Mauro. Exact Multivariate Bayesian Bootstrap Distributions of Moments. Ann. Statist. 23 (1995), no. 3, 762--768. doi:10.1214/aos/1176324620. https://projecteuclid.org/euclid.aos/1176324620


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