The Annals of Statistics

The Geometry of Mixture Likelihoods, Part II: The Exponential Family

Bruce G. Lindsay

Full-text: Open access

Abstract

Geometric analysis of the mixture likelihood set for univariate exponential family densities yields results which tie the number and location of support points for the nonparametric maximum likelihood estimator of the mixing distribution to sign changes in certain integrated polynomials. One corollary is a very general uniqueness theorem for the estimator.

Article information

Source
Ann. Statist. Volume 11, Number 3 (1983), 783-792.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
http://projecteuclid.org/euclid.aos/1176346245

Digital Object Identifier
doi:10.1214/aos/1176346245

Mathematical Reviews number (MathSciNet)
MR707929

Zentralblatt MATH identifier
0534.62002

JSTOR
links.jstor.org

Subjects
Primary: 62A10
Secondary: 62G05: Estimation 52A40: Inequalities and extremum problems 53A05: Surfaces in Euclidean space

Keywords
Mixture maximum likelihood curvature

Citation

Lindsay, Bruce G. The Geometry of Mixture Likelihoods, Part II: The Exponential Family. Ann. Statist. 11 (1983), no. 3, 783--792. doi:10.1214/aos/1176346245. http://projecteuclid.org/euclid.aos/1176346245.


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See also

  • Part I: Bruce G. Lindsay. The Geometry of Mixture Likelihoods: A General Theory. Ann. Statist., Volume 11, Number 1 (1983), 86--94.