A Uniform-in-P Edgeworth Expansion under Weak Cramér Conditions

06/04/2018

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by   Kyungchul Song, et al.

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This paper provides a finite sample bound for the error term in the Edgeworth expansion for a sum of independent, potentially discrete, nonlattice random vectors, using a uniform-in-P version of the weaker Cramér condition in Angst and Poly(2017). This finite sample bound is used to derive a bound for the error term in the Edgeworth expansion that is uniform over the joint distributions P of the random vectors, and eventually to derive a higher order expansion of resampling-based distributions in a unifying way. As an application, we derive a uniform-in-P Edgeworth expansion of bootstrap distributions and that of randomized subsampling distributions, when the joint distribution of the original sample is absolutely continuous with respect to Lebesgue measure.