Lower bounds on the approximation of the multivariate empirical process

DOI10.1007/BF02451433zbMath0554.60037OpenAlexW1994822781MaRDI QIDQ3217354

József Beck

Publication date: 1985

Published in: Unnamed Author (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02451433

zbMATH Keywords

Brownian bridgeempirical measure

Mathematics Subject Classification ID

Strong limit theorems (60F15) Brownian motion (60J65)

Related Items (9)

Local invariance principles and their application to density estimation ⋮ Kac's representation from an asymptotic viewpoint ⋮ Reminiscences, and some explorations about the bootstrap ⋮ Empirical and multiplier bootstraps for suprema of empirical processes of increasing complexity, and related Gaussian couplings ⋮ Nearly optimal central limit theorem and bootstrap approximations in high dimensions ⋮ Asymptotics for the critical level and a strong invariance principle for high intensity shot noise fields ⋮ Strong approximation for set-indexed partial sum processes via KMT constructions III ⋮ 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

Cites Work

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• On a problem of K. F. Roth concerning irregularities of point distribution
• On strong approximation of the multidimensional empirical process
• A remark on the approximation of the sample DF in the multidimensional case
• Central limit theorems for empirical measures
• Irregularities of distribution. IV
• An approximation of partial sums of independent RV'-s, and the sample DF. I
• A new method to prove strassen type laws of invariance principle. II
• On irregularities of distribution

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