Assessing the multivariate normal approximation of the maximum likelihood estimator from high-dimensional, heterogeneous data

Understand

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 vector parameter, and the multivariate normal distribution.
• We work with possibly high-dimensional, independent but not necessarily identically distributed random vectors.
• In addition, we obtain explicit upper bounds even in cases where the MLE cannot be expressed analytically.