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Bounds for the multivariate normal approximation of the maximum likelihood estimator

Research paper by Andreas Anastasiou

Indexed on: 13 Oct '15Published on: 13 Oct '15Published in: Mathematics - Statistics



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 possibly-high dimensional parameter, and the multivariate normal. An explicit analytical expression of the MLE is not required and the random vectors are independent but not necessarily identically distributed.