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

by   Andreas Anastasiou, et al.

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 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.



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