Functional laws of the iterated logarithm for local empirical processes indexed by sets

DOI10.1214/aop/1176988617zbMath0821.60042OpenAlexW1971167183MaRDI QIDQ1345614

David M. Mason, Paul Deheuvels

Publication date: 18 September 1995

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

Full work available at URL: https://doi.org/10.1214/aop/1176988617

zbMATH Keywords

functional laws of the iterated logarithmdensity estimationempirical measuresBahadur-Kiefer representationtail empirical processesDonsker classes

Mathematics Subject Classification ID

Asymptotic distribution theory in statistics (62E20) Central limit and other weak theorems (60F05) Order statistics; empirical distribution functions (62G30) Strong limit theorems (60F15) Functional limit theorems; invariance principles (60F17)

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Functional limit laws for the increments of Kaplan-Meier product-limit processes and applications ⋮ A uniform functional law of the logarithm for the local empirical process. ⋮ Nonstandard local empirical processes indexed by sets ⋮ Laws of the iterated logarithm for the local U-statistic process ⋮ A law of the iterated logarithm for Grenander's estimator ⋮ Some remarks on the uniform weak convergence of stochastic processes ⋮ Strong laws for local quantile processes ⋮ A law of the iterated logarithm for the empirical process based upon twice censored data ⋮ A note on a maximal Bernstein inequality ⋮ Central limit theorems for local empirical processes near boundaries of sets ⋮ Gaussian approximation of suprema of empirical processes ⋮ Nonstandard strong laws for local quantile processes ⋮ Some new almost sure results on the functional increments of the uniform empirical process ⋮ Differentiation of sets in measure ⋮ Local empirical processes near boundaries of convex bodies ⋮ Poisson and Gaussian approximation of weighted local empirical processes ⋮ A law of the iterated logarithm for wavelet density estimator ⋮ Nonparametric estimation of dichotomic regression with biomedical applications

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