First-order Edgeworth expansions with O(n^{-1}) remainders are established for general linear rank statistics via Stein's method and an extension of Bolthausen's combinatorial method.
A short proof of Motoo’s combinatorial central limit theorem using Stein’s method.Probab
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Edgeworth Expansions for Linear Rank Statistics -- Consolidated Version
First-order Edgeworth expansions with O(n^{-1}) remainders are established for general linear rank statistics via Stein's method and an extension of Bolthausen's combinatorial method.