Annals of Mathematical Statistics

Consistency and Asymptotic Normality of MLE's for Exponential Models

Robert H. Berk

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Abstract

Conditions are given for the strong consistency and asymptotic normality of the MLE (maximum likelihood estimator) for multiparameter exponential models. Because of the special structure assumed, the conditions are less restrictive than required by general theorems in this area. The technique involves certain convex functions on Euclidean spaces that arise naturally in the present context. Some examples are considered; among them, the multinomial distribution. Some convexity and continuity properties of multivariate cumulant generating functions are also discussed.

Article information

Source
Ann. Math. Statist., Volume 43, Number 1 (1972), 193-204.

Dates
First available in Project Euclid: 27 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aoms/1177692713

Digital Object Identifier
doi:10.1214/aoms/1177692713

Mathematical Reviews number (MathSciNet)
MR298810

Zentralblatt MATH identifier
0253.62005

JSTOR
links.jstor.org

Citation

Berk, Robert H. Consistency and Asymptotic Normality of MLE's for Exponential Models. Ann. Math. Statist. 43 (1972), no. 1, 193--204. doi:10.1214/aoms/1177692713. https://projecteuclid.org/euclid.aoms/1177692713


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