The Annals of Statistics

Mixtures of Distributions: A Topological Approach

L. A. Li and N. Sedransk

Full-text: Open access

Abstract

Identifiability problems have previously precluded a general approach to testing the hypothesis of a "pure" distribution against the alternative of a mixture of distributions. Three types of identifiability are defined, and it is shown that $B$-identifiability allows a Bayesian solution to the testing problem. First, an equivalence relation is defined over parametrizations of probability functions. Then the projection onto the quotient space is shown to give a $B$-identifiable parametrization. Bayesian inference proceeds using the Bayes factor as a "test" criterion.

Article information

Source
Ann. Statist., Volume 16, Number 4 (1988), 1623-1634.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176351057

Digital Object Identifier
doi:10.1214/aos/1176351057

Mathematical Reviews number (MathSciNet)
MR964942

Zentralblatt MATH identifier
0663.62021

JSTOR
links.jstor.org

Subjects
Primary: 62E10: Characterization and structure theory
Secondary: 62F03: Hypothesis testing 62F15: Bayesian inference

Keywords
Identifiability hypothesis testing detecting mixtures quotient space

Citation

Li, L. A.; Sedransk, N. Mixtures of Distributions: A Topological Approach. Ann. Statist. 16 (1988), no. 4, 1623--1634. doi:10.1214/aos/1176351057. https://projecteuclid.org/euclid.aos/1176351057


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