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Directional differentiability for supremum-type functionals: statistical applications. (English) Zbl 1442.62110

This paper proposes a very useful method for calculating the asymptotic distributions of various statistics in an objective way. This methodology is based on the Hadamard directional derivative and the Delta method. In particular, an application is presented for the asymptotic distribution of Kolmogorov-Smirnov type statistics under the alternative hypothesis. This article presents several inedited results and is relevant for researchers in the area of asymptotic distributions because the methodology developed has few restrictions and consequently can be applied to more contexts.

MSC:

62H05 Characterization and structure theory for multivariate probability distributions; copulas
62E20 Asymptotic distribution theory in statistics
62A01 Foundations and philosophical topics in statistics
62G20 Asymptotic properties of nonparametric inference

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EMD
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