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February 2020 Multivariate normal approximation of the maximum likelihood estimator via the delta method
Andreas Anastasiou, Robert E. Gaunt
Braz. J. Probab. Stat. 34(1): 136-149 (February 2020). DOI: 10.1214/18-BJPS411

Abstract

We use the delta method and Stein’s method to derive, under regularity conditions, explicit upper bounds for the distributional distance between the distribution of the maximum likelihood estimator (MLE) of a $d$-dimensional parameter and its asymptotic multivariate normal distribution. Our bounds apply in situations in which the MLE can be written as a function of a sum of i.i.d. $t$-dimensional random vectors. We apply our general bound to establish a bound for the multivariate normal approximation of the MLE of the normal distribution with unknown mean and variance.

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Andreas Anastasiou. Robert E. Gaunt. "Multivariate normal approximation of the maximum likelihood estimator via the delta method." Braz. J. Probab. Stat. 34 (1) 136 - 149, February 2020. https://doi.org/10.1214/18-BJPS411

Information

Received: 1 April 2017; Accepted: 1 August 2018; Published: February 2020
First available in Project Euclid: 3 February 2020

zbMATH: 07200396
MathSciNet: MR4058975
Digital Object Identifier: 10.1214/18-BJPS411

Rights: Copyright © 2020 Brazilian Statistical Association

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Vol.34 • No. 1 • February 2020
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