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February, 1972 Consistency and Asymptotic Normality of MLE's for Exponential Models
Robert H. Berk
Ann. Math. Statist. 43(1): 193-204 (February, 1972). DOI: 10.1214/aoms/1177692713


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.


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Robert H. Berk. "Consistency and Asymptotic Normality of MLE's for Exponential Models." Ann. Math. Statist. 43 (1) 193 - 204, February, 1972.


Published: February, 1972
First available in Project Euclid: 27 April 2007

MathSciNet: MR298810
zbMATH: 0253.62005
Digital Object Identifier: 10.1214/aoms/1177692713

Rights: Copyright © 1972 Institute of Mathematical Statistics

Vol.43 • No. 1 • February, 1972
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