Some new almost sure results on the functional increments of the uniform empirical process

DOI10.1016/j.spa.2010.11.006zbMath1218.60028arXiv1201.5516OpenAlexW2109266883MaRDI QIDQ550137

Davit Varron

Publication date: 8 July 2011

Published in: Stochastic Processes and their Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1201.5516

zbMATH Keywords

functional limit theoremsempirical processes

Mathematics Subject Classification ID

Asymptotic properties of nonparametric inference (62G20) Order statistics; empirical distribution functions (62G30) Functional limit theorems; invariance principles (60F17)

Related Items

Functional limit laws for local empirical processes in a spatial setting ⋮ Limit theorems for occupation rates of local empirical processes

Cites Work

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• Gaussian approximation of local empirical processes indexed by functions
• A refinement of the KMT inequality for the uniform empirical process
• A strong invariance theorem for the tail empirical process
• The a.s. behavior of the weighted empirical process and the LIL for the weighted tail empirical process
• Functional laws of the iterated logarithm for the increments of empirical and quantile processes
• Functional laws of the iterated logarithm for local empirical processes indexed by sets
• On the rate of clustering to the Strassen set for increments of the uniform empirical process
• The \(L_1\)-norm density estimator process
• Chung-type functional laws of the iterated logarithm for tail empirical processes
• Small ball probabilities for a shifted Poisson process
• Almost sure oscillation of certain random processes
• Some exact rates in the functional law of the iterated logarithm
• Strong approximation of quantile processes by iterated Kiefer processes.
• A uniform functional law of the logarithm for the local empirical process.
• Nonstandard local empirical processes indexed by sets
• Weak convergence and empirical processes. With applications to statistics
• Non standard functional limit laws for the increments of the compound empirical distribution function
• Inner rates of coverage of Strassen type sets by increments of the uniform empirical and quantile processes
• Small ball probabilities for a centered Poisson process of high intensity
• Nonstandard functional laws of the iterated logarithm for tail empirical and quantile processes
• A nonstandard uniform functional limit law for the increments of the multivariate empirical distribution function
• Asymptotic Statistics
• An empirical process approach to the uniform consistency of kernel-type function estimators