Explicit non-asymptotic bounds for the distance to the first-order Edgeworth expansion

Autor:	Derumigny, Alexis, Girard, Lucas, Guyonvarch, Yannick
Rok vydání:	2021
Předmět:	Mathematics - Probability Economics - Econometrics Mathematics - Statistics Theory Primary: 62E17 Secondary: 60F05 62F03
Druh dokumentu:	Working Paper
Popis:	In this article, we obtain explicit bounds on the uniform distance between the cumulative distribution function of a standardized sum $S_n$ of $n$ independent centered random variables with moments of order four and its first-order Edgeworth expansion. Those bounds are valid for any sample size with $n^{-1/2}$ rate under moment conditions only and $n^{-1}$ rate under additional regularity constraints on the tail behavior of the characteristic function of $S_n$. In both cases, the bounds are further sharpened if the variables involved in $S_n$ are unskewed. We also derive new Berry-Esseen-type bounds from our results and discuss their links with existing ones. We finally apply our results to illustrate the lack of finite-sample validity of one-sided tests based on the normal approximation of the mean. Comment: 51 pages, 2 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2101.05780 Zobrazit plný text záznamu View this record from Arxiv