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March, 1948 Asymptotic Properties of the Maximum Likelihood Estimate of an Unknown Parameter of a Discrete Stochastic Process
Abraham Wald
Ann. Math. Statist. 19(1): 40-46 (March, 1948). DOI: 10.1214/aoms/1177730288

Abstract

Asymptotic properties of maximum likelihood estimates have been studied so far mainly in the case of independent observations. In this paper the case of stochastically dependent observations is considered. It is shown that under certain restrictions on the joint probability distribution of the observations the maximum likelihood equation has at least one root which is a consistent estimate of the parameter $\theta$ to be estimated. Furthermore, any root of the maximum likelihood equation which is a consistent estimate of $\theta$ is shown to be asymptotically efficient. Since the maximum likelihood estimate is always a root of the maximum likelihood equation, consistency of the maximum likelihood estimate implies its asymptotic efficiency.

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Abraham Wald. "Asymptotic Properties of the Maximum Likelihood Estimate of an Unknown Parameter of a Discrete Stochastic Process." Ann. Math. Statist. 19 (1) 40 - 46, March, 1948. https://doi.org/10.1214/aoms/1177730288

Information

Published: March, 1948
First available in Project Euclid: 28 April 2007

zbMATH: 0032.17301
MathSciNet: MR24114
Digital Object Identifier: 10.1214/aoms/1177730288

Rights: Copyright © 1948 Institute of Mathematical Statistics

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Vol.19 • No. 1 • March, 1948
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