Strong approximation of quantile processes by iterated Kiefer processes.

DOI10.1214/aop/1019160265zbMath1044.60011OpenAlexW1488590818MaRDI QIDQ1872145

Paul Deheuvels

Publication date: 6 May 2003

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

Full work available at URL: https://doi.org/10.1214/aop/1019160265

zbMATH Keywords

order statisticsWiener processempirical processeslaw of the iterated logarithmquantile processesalmost sure convergencestrong approximationstrong lawsiterated Gaussian processesKiefer processesstrong invariance principlesBahadur-Kiefer-type theoremsiterated Wiener process

Mathematics Subject Classification ID

Gaussian processes (60G15) Asymptotic properties of nonparametric inference (62G20) Central limit and other weak theorems (60F05) Functional limit theorems; invariance principles (60F17)

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