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

05/11/2020

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by   Andreas Anastasiou, et al.

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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.