Rates of convergence in the central limit theorem for empirical processes

zbMath0615.60032MaRDI QIDQ1820496

Pascal Massart

Publication date: 1986

Published in: Annales de l'Institut Henri Poincaré. Probabilités et Statistiques (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=AIHPB_1986__22_4_381_0

zbMATH Keywords

empirical processesexponential inequalitiesweak and strong invariance principlesempirical Brownian bridge

Mathematics Subject Classification ID

Gaussian processes (60G15) Functional limit theorems; invariance principles (60F17)

Related Items (11)

Local invariance principles and their application to density estimation ⋮ On the limiting distributions of multivariate depth-based rank sum statistics and related tests ⋮ A Bernstein-type inequality for \(U\)-statistics and \(U\)-processes ⋮ Kac's representation from an asymptotic viewpoint ⋮ Strong averaging along foliated Lévy diffusions with heavy tails on compact leaves ⋮ Sharp tail distribution estimates for the supremum of a class of sums of i.i.d. random variables ⋮ Concentration Inequalities for Samples without Replacement ⋮ Flexible integrated functional depths ⋮ Accuracy of the approximation of an empirical process by a Brownian bridge ⋮ Komlós-Major-Tusnády approximation for the general empirical process and Haar expansions of classes of functions ⋮ Rate of convergence in the central limit theorem for empirical processes

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