The law of the iterated logarithm for empirical processes on Vapnik- Červonenkis classes

DOI10.1016/0047-259X(89)90093-6zbMath0688.60021MaRDI QIDQ1263867

Michel Talagrand, Kenneth S. Alexander

Publication date: 1989

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

zbMATH Keywords

empirical processlaw of iterated logarithmstochastic boundednessVapnik-Cervonenkis classes

Mathematics Subject Classification ID

Strong limit theorems (60F15) Limit theorems for vector-valued random variables (infinite-dimensional case) (60B12)

Related Items

On the law of the iterated logarithm for canonical \(U\)-statistics and processes, Point sets on the sphere \(\mathbb{S}^{2}\) with small spherical cap discrepancy, Estimation of complier expected shortfall treatment effects with a binary instrumental variable, Testing rationality without restricting heterogeneity, Bivariate estimation with left-truncated data, Sequential confidence bands for quantile densities under truncated and censored data, Tail bounds for the supremums of empirical processes over unbounded classes of functions, Sequential confidence bands for densities under truncated and censored data, A semiparametric model for truncated and censored data, Strong limit theorems for osciallation moduli of PL-process and cumulative hazard process under truncation and censorship with applications, A strong representation of the product-limit estimator for left truncated and right censored data

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• The central limit theorem for empirical processes on Vapnik- Červonenkis classes
• The central limit theorem for weighted empirical processes indexed by sets
• Probability inequalities for empirical processes and a law of the iterated logarithm
• Some limit theorems for empirical processes (with discussion)
• Unusual cluster sets for the LIL sequence in Banach space
• Characterization of the law of the iterated logarithm in Banach spaces
• On the weak convergence of empirical processes in sup-norm metrics
• A functional law of the iterated logarithm for weighted empirical distributions
• A strong convergence theorem for Banach space valued random variables
• Central limit theorems for empirical measures
• Comparison theorems, random geometry and some limit theorems for empirical processes
• Some results on the cluster set \(C(\{S_n/a_n\})\) and the LIL
• Sample functions of the Gaussian process
• Random Fourier Series with Applications to Harmonic Analysis. (AM-101)