Error bound in a central limit theorem of double-indexed permutation statistics

Lincheng Zhao, Zhidong Bai, Chern-Ching Chao, Wen-Qi Liang

Type: Article

Publication Date: 1997-10-01

Citations: 21

DOI: https://doi.org/10.1214/aos/1069362395

Abstract

An error bound in the normal approximation to the distribution of the double-indexed permutation statistics is derived. The derivation is based on Stein's method and on an extension of a combinatorial method of Bolthausen. The result can be applied to obtain the convergence rate of order $n^{-1/2}$ for some rank-related statistics, such as Kendall's tau, Spearman's rho and the Mann-Whitney-Wilcoxon statistic. Its applications to graph-related nonparametric statistics of multivariate observations are also mentioned.

Locations

The Annals of Statistics - View - PDF

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