The Annals of Statistics

Binomial mixtures: geometric estimation of the mixing distribution

G. R. Wood

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Abstract

Given a mixture of binomial distributions, how do we estimate the unknown mixing distribution? We build on earlier work of Lindsay and further elucidate the geometry underlying this question, exploring the approximating role played by cyclic polytopes. Convergence of a resulting maximum likelihood fitting algorithm is proved and numerical examples given; problems over the lack of identifiability of the mixing distribution in part disappear.

Article information

Source
Ann. Statist., Volume 27, Number 5 (1999), 1706-1721.

Dates
First available in Project Euclid: 23 September 2004

Permanent link to this document
https://projecteuclid.org/euclid.aos/1017939148

Digital Object Identifier
doi:10.1214/aos/1017939148

Mathematical Reviews number (MathSciNet)
MR2001a:62037

Zentralblatt MATH identifier
0955.62033

Subjects
Primary: 62G99: None of the above, but in this section
Secondary: 62P15: Applications to psychology 52B12: Special polytopes (linear programming, centrally symmetric, etc.)

Keywords
Binomial mixture mixing distribution geometry moment curve cyclic polytope nearest point least squares weighted least squares maximum likelihood Kullback-Leibler distance

Citation

Wood, G. R. Binomial mixtures: geometric estimation of the mixing distribution. Ann. Statist. 27 (1999), no. 5, 1706--1721. doi:10.1214/aos/1017939148. https://projecteuclid.org/euclid.aos/1017939148


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