## Electronic Journal of Statistics

### Assessing the multivariate normal approximation of the maximum likelihood estimator from high-dimensional, heterogeneous data

Andreas Anastasiou

#### Abstract

The asymptotic normality of the maximum likelihood estimator (MLE) under regularity conditions is a cornerstone of statistical theory. In this paper, we give explicit upper bounds on the distributional distance between the distribution of the MLE of a vector parameter, and the multivariate normal distribution. We work with possibly high-dimensional, independent but not necessarily identically distributed random vectors. In addition, we obtain upper bounds in cases where the MLE cannot be expressed analytically.

#### Article information

Source
Electron. J. Statist., Volume 12, Number 2 (2018), 3794-3828.

Dates
First available in Project Euclid: 30 November 2018

https://projecteuclid.org/euclid.ejs/1543568429

Digital Object Identifier
doi:10.1214/18-EJS1492

Mathematical Reviews number (MathSciNet)
MR3881763

Zentralblatt MATH identifier
06987203

Subjects
Primary: 62F12: Asymptotic properties of estimators
Secondary: 62E17: Approximations to distributions (nonasymptotic)

#### Citation

Anastasiou, Andreas. Assessing the multivariate normal approximation of the maximum likelihood estimator from high-dimensional, heterogeneous data. Electron. J. Statist. 12 (2018), no. 2, 3794--3828. doi:10.1214/18-EJS1492. https://projecteuclid.org/euclid.ejs/1543568429

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