A tail empirical process approach to some nonstandard laws of the iterated logarithm

DOI10.1007/BF01046994zbMath0719.60031MaRDI QIDQ2640223

Paul Deheuvels, David M. Mason

Publication date: 1991

Published in: Journal of Theoretical Probability (Search for Journal in Brave)

zbMATH Keywords

law of the iterated logarithmextreme value of a functional

Mathematics Subject Classification ID

Order statistics; empirical distribution functions (62G30) Strong limit theorems (60F15)

Related Items (10)

Functional limit laws for the increments of Kaplan-Meier product-limit processes and applications ⋮ Nonstandard local empirical processes indexed by sets ⋮ A functional law of the iterated logarithm for the Dekkers-Einmahl-de Haan tail index estimator ⋮ Erdős-Rényi-Type Functional Limit Laws for Renewal Processes ⋮ Central limit theorems for local empirical processes near boundaries of sets ⋮ Some asymptotic results on density estimators by wavelet projections ⋮ A functional law of the iterated logarithm for tail quantile processes ⋮ Nonstandard strong laws for local quantile processes ⋮ A functional law of the iterated logarithm for the dekkers-einmahl-de haan tail index estimator ⋮ Poisson and Gaussian approximation of weighted local empirical processes

Cites Work

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• A strong limit theorem for the oscillation modulus of the uniform empirical quantile process
• Strong laws for the k-th order statistic when k\(\leq c\,\log _ 2\,n\)
• A simple general approach to inference about the tail of a distribution
• Functional laws of the iterated logarithm for the partial sums of i.i.d. random variables in the asymmetric stable law
• A functional law of the iterated logarithm for weighted empirical distributions
• Nonstandard functional laws of the iterated logarithm for tail empirical and quantile processes
• Almost sure convergence of the Hill estimator
• Toward a universal law of the iterated logarithm, Part II
• Strong limit theorems for oscillation moduli of the uniform empirical process
• The Law of the Iterated Logarithm for Empirical Distribution
• Large deviations for processes with independent increments

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