B0658
Title: Wasserstein distance error bounds for the normal approximation of the maximum likelihood estimator
Authors: Robert Gaunt - The University of Manchester (United Kingdom) [presenting]
Abstract: Explicit Wasserstein distance error bounds between the distribution of the multi-parameter MLE and the multivariate normal distribution are presented. Our general bounds are given for possibly high-dimensional, independent and identically distributed random vectors, and are of the optimal order with respect to the sample size n. In deriving these bounds, we make use of recent advances from Stein's method literature concerning optimal order Wasserstein distance bounds in the multivariate central limit theorem. As concrete examples, we use our general bounds to obtain Wasserstein distance error bounds for the normal/multivariate normal approximation of the MLE for the exponential distribution under canonical parameterisation and the normal distribution under canonical parametrisation.
