Functional central limit theorems for triangular arrays of function-indexed processes under uniformly integrable entropy conditions

DOI10.1006/jmva.1997.1688zbMath0895.60035OpenAlexW2045345498MaRDI QIDQ1368844

Klaus Ziegler

Publication date: 1 October 1997

Published in: Journal of Multivariate Analysis (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/401db9a12c5923f60c04bad7b4626a99c9296931

zbMATH Keywords

functional central limit theoremsmaximal inequalitytriangular arraysintensity estimationsmoothing by convolutionrandom measure processesspatial Poisson processes

Mathematics Subject Classification ID

Density estimation (62G07) Nonparametric estimation (62G05) Sums of independent random variables; random walks (60G50) Functional limit theorems; invariance principles (60F17)

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Cites Work

• The central limit theorem for empirical processes on Vapnik- Červonenkis classes
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• Some limit theorems for empirical processes (with discussion)
• Some new Vapnik-Chervonenkis classes
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• Lévy's Brownian motion as a set-indexed process and a related central limit theorem
• Central limit theorems for stochastic processes under random entropy conditions
• A uniform central limit theorem for set-indexed partial-sum processes with finite variance
• Characterization of the law of the iterated logarithm in Banach spaces
• A central limit theorem under metric entropy with \(L_ 2\) bracketing
• Weak convergence of the empirical characteristic function
• Uniform Donsker classes of functions
• Central limit theorems for empirical measures
• Nonparametric model checks for regression
• Comparison theorems, random geometry and some limit theorems for empirical processes
• Weak convergence and empirical processes. With applications to statistics
• On the Uniform Convergence of Relative Frequencies of Events to Their Probabilities
• Convergence of stochastic processes
• Uniform laws of large numbers for triangular arrays of function-indexed processes under random entropy conditions
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