Functional laws of the iterated logarithm for small increments of empirical processes

DOI10.1111/j.1467-9574.1996.tb01493.xzbMath0862.60023OpenAlexW2014992712MaRDI QIDQ4715804

Paul Deheuvels

Publication date: 25 May 1997

Published in: Statistica Neerlandica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1111/j.1467-9574.1996.tb01493.x

zbMATH Keywords

weak topologylarge incrementsalmost sure limiting behaviourHausdorff set-metric

Mathematics Subject Classification ID

Order statistics; empirical distribution functions (62G30) Strong limit theorems (60F15) Functional limit theorems; invariance principles (60F17)

Related Items (4)

Functional limit laws for the increments of Kaplan-Meier product-limit processes and applications ⋮ Some more results on increments of the partially observed empirical process. ⋮ Functional Chung laws for small increments of the empirical process and a lowerbound in the strong invariance principle ⋮ Nonstandard strong laws for local quantile processes

Cites Work

• A strong limit theorem for the oscillation modulus of the uniform empirical quantile process
• The almost sure behavior of maximal and minimal multivariate \(k_ n\)- spacings
• The oscillation behavior of empirical processes
• A functional law of the iterated logarithm for tail quantile processes
• Functional laws of the iterated logarithm for the increments of empirical and quantile processes
• Functional laws of the iterated logarithm for large increments of empirical and quantile processes
• Transformations in functional iterated logarithm laws and regular variation
• On the fractal nature of empirical increments
• Nonstandard functional laws of the iterated logarithm for tail empirical and quantile processes
• Strong laws for the maximal k-spacing when k?c log n
• Upper and lower class sequences for minimal uniform spacings
• Strong limit theorems for oscillation moduli of the uniform empirical process
• On the Rate of Growth of the Partial Maxima of a Sequence of Independent Identically Distributed Random Variables.
• A Measure of Asymptotic Efficiency for Tests of a Hypothesis Based on the sum of Observations

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