Binomial mixtures

Geometric estimation of the mixing distribution

G. R. Wood*

*Corresponding author for this work

    Research output: Contribution to journalArticle

    13 Citations (Scopus)

    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.

    Original languageEnglish
    Pages (from-to)1706-1721
    Number of pages16
    JournalAnnals of Statistics
    Volume27
    Issue number5
    Publication statusPublished - Oct 1999

    Keywords

    • Binomial
    • Cyclic polytope
    • Geometry
    • Kullback - Leibler distance
    • Least squares
    • Maximum likelihood
    • Mixing distribution
    • Mixture
    • Moment curve
    • Nearest point
    • Weighted least squares

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