Bounds for the multivariate normal approximation of the maximum likelihood estimator

Andreas Anastasiou

Published 2015-10-13Version 1

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.