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A multivariate Bahadur-Kiefer representation for the empirical Copula process. (English) Zbl 1288.60034

J. Math. Sci., New York 163, No. 4, 382-398 (2009) and Zap. Nauchn. Semin. POMI 364, 120-147 (2009).
Summary: We provide a multivariate extension of [J. Kiefer “Deviations between the sample quantile process and the sample \(df\)”, in: Nonparametric techniques in statistical inference. Cambridge: University Press. 299–319 (1970)] strong limit law for the uniform Bahadur-Kiefer representation. This allows us to derive optimal rates for the strong approximation of empirical copula processes by sequences of Gaussian processes. We also provide a Hill characterization of empirical copulas in a general framework.

MSC:

60F15 Strong limit theorems
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