Annals of Statistics

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

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

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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.

Article information

Ann. Statist., Volume 25, Number 5 (1997), 2210-2227.

First available in Project Euclid: 20 November 2003

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60F05: Central limit and other weak theorems 62E20: Asymptotic distribution theory
Secondary: 62H20: Measures of association (correlation, canonical correlation, etc.)

Asymptotic normality correlation coefficient graph theory multivariate association permutation statistics Stein's method


Zhao, Lincheng; Bai, Zhidong; Chao, Chern-Ching; Liang, Wen-Qi. Error bound in a central limit theorem of double-indexed permutation statistics. Ann. Statist. 25 (1997), no. 5, 2210--2227. doi:10.1214/aos/1069362395.

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