文章基本信息

标题：Bounds for the asymptotic normality of the maximum likelihood estimator using the Delta method
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作者：Andreas Anastasiou ; Christophe Ley
期刊名称：Latin American Journal of Probability and Mathematical Statistics
电子版ISSN：1980-0436
出版年度：2017
卷号：XIV
页码：153-171
出版社：Instituto Nacional De Matemática Pura E Aplicada
摘要：The asymptotic normality of the Maximum Likelihood Estimator(MLE) is a cornerstone of statistical theory. In the present paper, we providesharp explicit upper bounds on Zolotarev-type distances between the exact, unknowndistribution of the MLE and its limiting normal distribution. Our approachto this fundamental issue is based on a sound combination of the Delta method,Stein’s method, Taylor expansions and conditional expectations, for the classicalsituations where the MLE can be expressed as a function of a sum of independentand identically distributed terms. This result is tailored for the broad class ofone-parameter exponential family distributions.
关键词：Delta method; Maximum likelihood estimator; Normal approximation;Stein’s method.