Open Access
June, 1991 On Maximum Likelihood Estimation in Infinite Dimensional Parameter Spaces
Wing Hung Wong, Thomas A. Severini
Ann. Statist. 19(2): 603-632 (June, 1991). DOI: 10.1214/aos/1176348113


An approximate maximum likelihood estimate is known to be consistent under some compactness and integrability conditions. In this paper we study its convergence rate and its asymptotic efficiency in estimating smooth functionals of the parameter. We provide conditions under which the rate of convergence can be established. This rate is essentially governed by the size of the space of score functions as measured by an entropy index. We also show that, for a large class of smooth functionals, the plug-in maximum likelihood estimate is asymptotically efficient, that is, it achieves the minimal Fisher information bound. The theory is illustrated by several nonparametric or semiparametric examples.


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Wing Hung Wong. Thomas A. Severini. "On Maximum Likelihood Estimation in Infinite Dimensional Parameter Spaces." Ann. Statist. 19 (2) 603 - 632, June, 1991.


Published: June, 1991
First available in Project Euclid: 12 April 2007

zbMATH: 0732.62026
MathSciNet: MR1105838
Digital Object Identifier: 10.1214/aos/1176348113

Primary: 62F12
Secondary: 62G20

Keywords: convergence rate , efficiency , maximum likelihood , nonparametric , semiparametric

Rights: Copyright © 1991 Institute of Mathematical Statistics

Vol.19 • No. 2 • June, 1991
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