2015/08/20 by Andreas Anastasiou, Christophe Ley, Anastasiou, Andreas +1
Computer Science · Mathematics · #Bayesian Methods and Mixture Models #FOS: Mathematics #Statistical Distribution Estimation and Applications #Statistical Methods and Bayesian Inference #Statistics Theory (math.ST) #math.ST #stat.TH
paper · pdf · doi:10.48550/arxiv.1508.04948
15 pages, 1 table
openalex publication_date 2015/08/20 · arxiv created 2016/04/17 · arxiv updated 2016/04/19 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28
The asymptotic normality of the Maximum Likelihood Estimator (MLE) is a cornerstone of statistical theory. In the present paper, we provide sharp explicit upper bounds on Zolotarev-type distances between the exact, unknown distribution of the MLE and its limiting normal distribution. Our approach to this fundamental issue is based on a sound combination of the Delta method, Stein's method, Taylor expansions and conditional expectations, for the classical situations where the MLE can be expressed as a function of a sum of independent and identically distributed terms. This encompasses in particular the broad exponential family of distributions.