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 language | English |
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Pages (from-to) | 1706-1721 |
Number of pages | 16 |
Journal | Annals of Statistics |
Volume | 27 |
Issue number | 5 |
Publication status | Published - Oct 1999 |
Keywords
- Binomial
- Cyclic polytope
- Geometry
- Kullback - Leibler distance
- Least squares
- Maximum likelihood
- Mixing distribution
- Mixture
- Moment curve
- Nearest point
- Weighted least squares