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Normal approximation for nonlinear statistics using a concentration inequality approach. (English) Zbl 1146.62310

Summary: Let \(T\) be a general sampling statistic that can be written as a linear statistic plus an error term. Uniform and non-uniform Berry-Esseen type bounds for \(T\) are obtained. The bounds are the best possible for many known statistics. Applications to \(U\)-statistics, multisample \(U\)-statistics, \(L\)-statistics, random sums and functions of nonlinear statistics are discussed.

MSC:

62E17 Approximations to statistical distributions (nonasymptotic)
60E15 Inequalities; stochastic orderings
62G99 Nonparametric inference
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