Berry-Esseen-Type Bounds for Signed Linear Rank Statistics with a Broad Range of Scores
The Annals of Statistics · 1990 · Volume 18 · Issue 3
Abstract
The Berry-Esseen-type bounds of order $N^{-1/2}$ for the rate of convergence to normality are derived for the signed linear rank statistics under the hypothesis of symmetry. The results are obtained with a broad range of regression constants and scores (allowed to be generated by discontinuous score generating functions, but not necessarily) restricted by only mild conditions, while almost all previous results are obtained with continuously differentiable score generating functions. Furthermore, the proof is very short and elementary, based on the conditioning argument.
Keywords
60F05, 62E20, 62G10, Berry-Esseen bound, discontinuous score generating function, rate of convergence, signed linear rank statistic
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