# Wasserstein distance error bounds for the multivariate normal approximation of the maximum likelihood estimator

Research paper by Andreas Anastasiou, Robert E. Gaunt

Indexed on: 12 May '20Published on: 11 May '20Published in: arXiv - Mathematics - Statistics

#### Abstract

We obtain explicit Wasserstein distance error bounds between the distribution of the multi-parameter MLE and the multivariate normal distribution. Our general bounds are given for possibly high-dimensional, independent and identically distributed random vectors. Our general bounds are of the optimal $\mathcal{O}(n^{-1/2})$ order. We apply our general bounds to derive Wasserstein distance error bounds for the multivariate normal approximation of the MLE in several settings; these being single-parameter exponential families, the normal distribution under canonical parametrisation, and the multivariate normal distribution under non-canonical parametrisation.