Open Access
February 2017 Bounds for the normal approximation of the maximum likelihood estimator
Andreas Anastasiou, Gesine Reinert
Bernoulli 23(1): 191-218 (February 2017). DOI: 10.3150/15-BEJ741


While the asymptotic normality of the maximum likelihood estimator under regularity conditions is long established, this paper derives explicit bounds for the bounded Wasserstein distance between the distribution of the maximum likelihood estimator (MLE) and the normal distribution. For this task, we employ Stein’s method. We focus on independent and identically distributed random variables, covering both discrete and continuous distributions as well as exponential and non-exponential families. In particular, a closed form expression of the MLE is not required. We also use a perturbation method to treat cases where the MLE has positive probability of being on the boundary of the parameter space.


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Andreas Anastasiou. Gesine Reinert. "Bounds for the normal approximation of the maximum likelihood estimator." Bernoulli 23 (1) 191 - 218, February 2017.


Received: 1 December 2014; Revised: 1 June 2015; Published: February 2017
First available in Project Euclid: 27 September 2016

zbMATH: 1362.60017
MathSciNet: MR3556771
Digital Object Identifier: 10.3150/15-BEJ741

Keywords: maximum likelihood estimator , Normal approximation , Stein’s method

Rights: Copyright © 2017 Bernoulli Society for Mathematical Statistics and Probability

Vol.23 • No. 1 • February 2017
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