Strong approximation for set-indexed partial sum processes via KMT constructions. I

DOI10.1214/aop/1176989266zbMath0776.60045OpenAlexW4247567605MaRDI QIDQ686761

Emmanuel Rio

Publication date: 11 October 1993

Published in: The Annals of Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1214/aop/1176989266

zbMATH Keywords

central limit theoreminvariance principlestrong approximationmetric entropyrandom measureset-indexed processVapnik-Chervonenkis class

Mathematics Subject Classification ID

Functional limit theorems; invariance principles (60F17) Nonparametric inference (62G99)

Related Items (14)

Local invariance principles and their application to density estimation ⋮ CLT for linear random fields with stationary martingale-difference innovation ⋮ Invariance principles for generalized domains of semistable attraction ⋮ Strong approximation for set-indexed partial sum processes via KMT constructions III ⋮ On bootstrapping panel factor series ⋮ Asymptotics for linear random fields ⋮ Maxima of asymptotically Gaussian random fields and moderate deviation approximations to boundary crossing probabilities of sums of random variables with multidimensional indices ⋮ Upper bounds for minimal distances in the central limit theorem ⋮ On confidence bands for multivariate nonparametric regression ⋮ Unnamed Item ⋮ Convergence of weighted partial sums when the limiting distribution is not necessarily Radon ⋮ Confidence bands for multivariate and time dependent inverse regression models ⋮ The accuracy of strong Gaussian approximation for sums of independent random vectors ⋮ Komlós-Major-Tusnády approximation for the general empirical process and Haar expansions of classes of functions

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