The Annals of Statistics

Approximate Bayes Solutions to Some Nonparametric Problems

M. Goldstein

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Abstract

The problem of making inferences about real functions of a probability distribution of unknown form is examined in a Bayesian nonparameteric framework. With respect to a general quadratic loss function, Bayes estimates within the class of linear combinations of a given set of functions on the sample space are obtained for general functions on the distribution space. The result is then used to derive Bayes polynomial estimates of the moments of the distribution.

Article information

Source
Ann. Statist., Volume 3, Number 2 (1975), 512-517.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176343081

Digital Object Identifier
doi:10.1214/aos/1176343081

Mathematical Reviews number (MathSciNet)
MR362702

Zentralblatt MATH identifier
0325.62032

JSTOR
links.jstor.org

Subjects
Primary: 62C10: Bayesian problems; characterization of Bayes procedures
Secondary: 62G05: Estimation

Keywords
Bayes nonparametric estimation linear approximation polynomial estimators for population moments

Citation

Goldstein, M. Approximate Bayes Solutions to Some Nonparametric Problems. Ann. Statist. 3 (1975), no. 2, 512--517. doi:10.1214/aos/1176343081. https://projecteuclid.org/euclid.aos/1176343081


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