The rate of convergence for multivariate sampling statistics. (English) Zbl 0798.62023

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)


62E20 Asymptotic distribution theory in statistics
60F05 Central limit and other weak theorems
62G99 Nonparametric inference
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