Papers › Explicit non-asymptotic bounds for the distance to the first-order Edgeworth expansion
Explicit non-asymptotic bounds for the distance to the first-order Edgeworth expansion
Alexis Derumigny, Lucas Girard, Yannick Guyonvarch
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In this article, we obtain explicit bounds on the uniform distance between the cumulative distribution function of a standardized sum Sₙ 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 Sₙ. In both cases, the bounds are further sharpened if the variables involved in Sₙ 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.
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