## Annals of Statistics

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

#### 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.

#### Article information

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

Dates
First available in Project Euclid: 20 November 2003

https://projecteuclid.org/euclid.aos/1069362395

Digital Object Identifier
doi:10.1214/aos/1069362395

Mathematical Reviews number (MathSciNet)
MR1474091

Zentralblatt MATH identifier
0897.60024

#### Citation

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. https://projecteuclid.org/euclid.aos/1069362395