The central limit theorem for empirical processes on V-Č classes: A majorizing measure approach

DOI10.1007/BF02562693zbMath0833.60036MaRDI QIDQ1346933

Juan J. Romo

Publication date: 10 May 1995

Published in: Test (Search for Journal in Brave)

zbMATH Keywords

majorizing measuresVapnik-Cervonenkis classescentral limit theorem for empirical processes

Mathematics Subject Classification ID

Functional limit theorems; invariance principles (60F17) Limit theorems for vector-valued random variables (infinite-dimensional case) (60B12)

Cites Work

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• The central limit theorem for empirical processes on Vapnik- Červonenkis classes
• Regularity of Gaussian processes
• Some limit theorems for empirical processes (with discussion)
• A uniform central limit theorem for set-indexed partial-sum processes with finite variance
• A central limit theorem under metric entropy with \(L_ 2\) bracketing
• The central limit theorem and the law of iterated logarithm for empirical processes under local conditions
• The sizes of compact subsets of Hilbert space and continuity of Gaussian processes
• Sample functions of the Gaussian process
• Continuity Properties of Some Gaussian Processes
• Probability Inequalities for the Sum of Independent Random Variables
• Law of the iterated logarithm for set-indexed partial sum processes with finite variance
• The Central Limit Theorem for Empirical Processes Under Local Conditions: The Case of Radon Infinitely Divisible Limits without Gaussian Component
• Probability Inequalities for Sums of Bounded Random Variables
• On the Uniform Convergence of Relative Frequencies of Events to Their Probabilities
• Convergence of stochastic processes

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