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arXiv · 1508.04948

Bounds for the asymptotic normality of the maximum likelihood estimator using the Delta method

Andreas Anastasiou·Christophe Ley
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Abstract

The asymptotic normality of the Maximum Likelihood Estimator (MLE) is a cornerstone of statistical theory. In the present paper, we provide sharp explicit upper bounds on Zolotarev-type distances between the exact, unknown distribution of the MLE and its limiting normal distribution. Our approach to this fundamental issue is based on a sound combination of the Delta method, Stein's method, Taylor expansions and conditional expectations, for the classical situations where the MLE can be expressed as a function of a sum of independent and identically distributed terms. This encompasses in particular the broad exponential family of distributions.

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Andreas Anastasiou, Christophe Ley. 2016-04-17. Bounds for the asymptotic normality of the maximum likelihood estimator using the Delta method. https://arxiv.org/abs/1508.04948

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