Bolthausen, Erwin; Götze, Friedrich The rate of convergence for multivariate sampling statistics. (English) Zbl 0798.62023 Ann. Stat. 21, No. 4, 1692-1710 (1993). From the authors’ summary: A Berry-Esseen theorem for the rate of convergence of general nonlinear multivariate sampling statistics with normal limit distribution is derived via a multivariate extension of Stein’s method. The result generalizes in particular previous results of the first author for one-dimensional linear rank statistics and one- dimensional results of van Zwet et al. for general functions of independent random elements, and provides convergence bounds for general multivariate sampling statistics without restrictions on the sampling proportions. Reviewer: G.Roussas (Davis) Cited in 17 Documents MSC: 62E20 Asymptotic distribution theory in statistics 60F05 Central limit and other weak theorems 62G99 Nonparametric inference Keywords:multivariate central limit theorem; Berry-Esseen theorem; rate of convergence; general nonlinear multivariate sampling statistics; normal limit distribution; multivariate extension of Stein’s method; linear rank statistics; general functions of independent random elements; convergence bounds × Cite Format Result Cite Review PDF Full Text: DOI