The Annals of Statistics

Uniform Asymptotic Normality of the Maximum Likelihood Estimator

T. J. Sweeting

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Abstract

A very general result concerning the weak consistency and uniform asymptotic normality of the maximum likelihood estimator is presented. The result proves to be of particular value in establishing uniform asymptotic normality of randomly normalized maximum likelihood estimators of parameters in stochastic processes. The only conditions imposed are certain regularity conditions on the (random) information function, easily verified in practice. Application of the result is briefly considered.

Article information

Source
Ann. Statist., Volume 8, Number 6 (1980), 1375-1381.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176345208

Digital Object Identifier
doi:10.1214/aos/1176345208

Mathematical Reviews number (MathSciNet)
MR594652

Zentralblatt MATH identifier
0447.62041

JSTOR
links.jstor.org

Subjects
Primary: 62E20: Asymptotic distribution theory
Secondary: 62M99: None of the above, but in this section

Keywords
Uniform asymptotic normality maximum likelihood estimation inference from stochastic processes

Citation

Sweeting, T. J. Uniform Asymptotic Normality of the Maximum Likelihood Estimator. Ann. Statist. 8 (1980), no. 6, 1375--1381. doi:10.1214/aos/1176345208. https://projecteuclid.org/euclid.aos/1176345208


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Corrections

  • See Correction: T. J. Sweeting. Corrections: Uniform Asymptotic Normality of the Maximum Likelihood Estimator. Ann. Statist., Volume 10, Number 1 (1982), 320--320.