Translator Disclaimer
September, 1985 Strong Consistency of Approximate Maximum Likelihood Estimators with Applications in Nonparametrics
Jane-Ling Wang
Ann. Statist. 13(3): 932-946 (September, 1985). DOI: 10.1214/aos/1176349647

Abstract

Wald's general analytic conditions that imply strong consistency of the approximate maximum likelihood estimators (AMLEs) have been extended by Le Cam, Kiefer and Wolfowitz, Huber, Bahadur, and Perlman. All these conditions use the log likelihood ratio of the type $\log\lbrack f(x, \theta)/f(x, \theta_0)\rbrack$, where $\theta_0$ is the true value of the parameter. However these methods usually fail in the nonparametric case. Thus, in this paper, for each $\theta \neq \theta_0$, we look at the log likelihood ratio of the type $\log\lbrack f(x, \theta)/f(x, \theta_r(\theta))\rbrack$, where $\theta_r(\theta)$ is a certain parameter selected in a neighborhood $V_r$ of $\theta_0$. Some general analytic conditions that imply strong consistency of the AMLE are given. The results are shown to be applicable to several nonparametric families having densities, e.g., concave distributions functions, and increasing failure rate distributions. In particular, they can be applied to several censored data cases.

Citation

Download Citation

Jane-Ling Wang. "Strong Consistency of Approximate Maximum Likelihood Estimators with Applications in Nonparametrics." Ann. Statist. 13 (3) 932 - 946, September, 1985. https://doi.org/10.1214/aos/1176349647

Information

Published: September, 1985
First available in Project Euclid: 12 April 2007

zbMATH: 0598.62034
MathSciNet: MR803749
Digital Object Identifier: 10.1214/aos/1176349647

Subjects:
Primary: 62F12
Secondary: 60F15, 62G05

Rights: Copyright © 1985 Institute of Mathematical Statistics

JOURNAL ARTICLE
15 PAGES


SHARE
Vol.13 • No. 3 • September, 1985
Back to Top