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- W4295358001 abstract "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." @default.
- W4295358001 created "2022-09-13" @default.
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- W4295358001 date "2021-01-14" @default.
- W4295358001 modified "2023-09-26" @default.
- W4295358001 title "Explicit non-asymptotic bounds for the distance to the first-order Edgeworth expansion" @default.
- W4295358001 doi "https://doi.org/10.48550/arxiv.2101.05780" @default.
- W4295358001 hasPublicationYear "2021" @default.
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