The Annals of Statistics

Maximum likelihood estimates via duality for log-convex models when cell probabilities are subject to convex constraints

Richard Dykstra and Hammou El Barmi

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Abstract

The purpose of this article is to derive and illustrate a method for fitting models involving both convex and log-convex constraints on the probability vector(s) of a (product) multinomial distribution. We give a two-step algorithm to obtain maximum likelihood estimates of the probability vector(s) and show that it is guaranteed to converge to the true solution. Some examples are discussed which illustrate the procedure.

Article information

Source
Ann. Statist., Volume 26, Number 5 (1998), 1878-1893.

Dates
First available in Project Euclid: 21 June 2002

Permanent link to this document
https://projecteuclid.org/euclid.aos/1024691361

Digital Object Identifier
doi:10.1214/aos/1024691361

Mathematical Reviews number (MathSciNet)
MR1673282

Zentralblatt MATH identifier
0929.62029

Subjects
Primary: 62F30: Inference under constraints
Secondary: 62G05

Keywords
Convex constraints log-convex constraints maximum likelihood multinomial iterative algorithm $ I$-projection duality convex cones

Citation

El Barmi, Hammou; Dykstra, Richard. Maximum likelihood estimates via duality for log-convex models when cell probabilities are subject to convex constraints. Ann. Statist. 26 (1998), no. 5, 1878--1893. doi:10.1214/aos/1024691361. https://projecteuclid.org/euclid.aos/1024691361


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  • MANHATTAN, KANSAS 66506 UNIVERSITY OF IOWA E-MAIL: barmi@stat.ksu.edu IOWA CITY, IOWA 52242-1419 E-MAIL: dy kstra@stat.uiowa.edu