Error bound in a central limit theorem of double-indexed permutation statistics
Zhao, Lincheng ; Bai, Zhidong ; Chao, Chern-Ching ; Liang, Wen-Qi
Ann. Statist., Tome 25 (1997) no. 6, p. 2210-2227 / Harvested from Project Euclid
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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.
Publié le : 1997-10-14
Classification:  Asymptotic normality,  correlation coefficient,  graph theory,  multivariate association,  permutation statistics,  Stein's method,  60F05,  62E20,  62H20 
@article{1069362395,
     author = {Zhao, Lincheng and Bai, Zhidong and Chao, Chern-Ching and Liang, Wen-Qi},
     title = {Error bound in a central limit theorem of double-indexed permutation statistics},
     journal = {Ann. Statist.},
     volume = {25},
     number = {6},
     year = {1997},
     pages = { 2210-2227},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1069362395}
}

Zhao, Lincheng; Bai, Zhidong; Chao, Chern-Ching; Liang, Wen-Qi. Error bound in a central limit theorem of double-indexed permutation statistics. Ann. Statist., Tome 25 (1997) no. 6, pp.  2210-2227. http://gdmltest.u-ga.fr/item/1069362395/