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

• 成果类型: Article
• 署名作者: Zhao, LC; Bai, ZD; Chao, CC; Liang, WQ
• 署名单位: Chinese Academy of Sciences; University of Science & Technology of China, CAS; National Sun Yat Sen University; Academia Sinica - Taiwan
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1069362395
• 发表日期: 1997
• 页码: 2210-2227
• 关键词: 2-sample tests; MULTIVARIATE; association

摘要

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.