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October 1997 Error bound in a central limit theorem of double-indexed permutation statistics
Lincheng Zhao, Zhidong Bai, Chern-Ching Chao, Wen-Qi Liang
Ann. Statist. 25(5): 2210-2227 (October 1997). DOI: 10.1214/aos/1069362395


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.


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Lincheng Zhao. Zhidong Bai. Chern-Ching Chao. Wen-Qi Liang. "Error bound in a central limit theorem of double-indexed permutation statistics." Ann. Statist. 25 (5) 2210 - 2227, October 1997.


Published: October 1997
First available in Project Euclid: 20 November 2003

zbMATH: 0897.60024
MathSciNet: MR1474091
Digital Object Identifier: 10.1214/aos/1069362395

Primary: 60F05 , 62E20
Secondary: 62H20

Keywords: asymptotic normality , correlation coefficient , graph theory , Multivariate association , permutation statistics , Stein's method

Rights: Copyright © 1997 Institute of Mathematical Statistics


Vol.25 • No. 5 • October 1997
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