Bounds for the normal approximation of the maximum likelihood estimator from m-dependent random variables

TL;DR

This paper extends the understanding of the maximum likelihood estimator's normal approximation by providing explicit bounds under local dependence structures, specifically for m-dependent random variables, using the Wasserstein metric.

Contribution

It introduces bounds for the MLE's distributional distance to normality in the context of m-dependent variables, expanding previous independent case results.

Findings

Provides explicit Wasserstein bounds for MLE under m-dependence

Extends normal approximation results to dependent data structures

Enhances understanding of MLE behavior in dependent settings

Abstract

The asymptotic normality of the Maximum Likelihood Estimator (MLE) is a long established result. Explicit bounds for the distributional distance between the distribution of the MLE and the normal distribution have recently been obtained for the case of independent random variables. In this paper, a local dependence structure is introduced between the random variables and we give upper bounds which are specified for the Wasserstein metric.