A note on uniform laws of averages for dependent processes

DOI10.1016/0167-7152(93)90163-DzbMath0776.60042MaRDI QIDQ1801875

Amir Dembo, Andrew B. Nobel

Publication date: 24 November 1993

Published in: Statistics \& Probability Letters (Search for Journal in Brave)

zbMATH Keywords

uniform convergenceregularity conditionsweak Bernoulli processespermissible class

Mathematics Subject Classification ID

Strong limit theorems (60F15) Zero-one laws (60F20) Limit theorems for vector-valued random variables (infinite-dimensional case) (60B12)

Related Items (19)

Some Characteristics of the Conditional Set-Indexed Empirical Process Involving Functional Ergodic Data ⋮ A counterexample concerning uniform ergodic theorems for a class of functions ⋮ A Strong Law of Large Numbers for Strongly Mixing Processes ⋮ Generalization bounds of ERM algorithm with Markov chain samples ⋮ Learning performance of Tikhonov regularization algorithm with geometrically beta-mixing observations ⋮ Random Forests for Spatially Dependent Data ⋮ The generalization performance of ERM algorithm with strongly mixing observations ⋮ The performance bounds of learning machines based on exponentially strongly mixing sequences ⋮ Unsupervised slow subspace-learning from stationary processes ⋮ Sequential complexities and uniform martingale laws of large numbers ⋮ Uniform convergence of Vapnik-Chervonenkis classes under ergodic sampling ⋮ Statistics of Robust Optimization: A Generalized Empirical Likelihood Approach ⋮ Testing linearity against threshold effects: uniform inference in quantile regression ⋮ Estimating tail decay for stationary sequences via extreme values ⋮ Statistical and Computational Guarantees for the Baum-Welch Algorithm ⋮ Unnamed Item ⋮ Central limit theorems for empirical and \(U\)-processes of stationary mixing sequences ⋮ Rates of uniform convergence of empirical means with mixing processes ⋮ Some remarks on coupling of dependent random variables

Cites Work

• Probability inequalities for empirical processes and a law of the iterated logarithm
• Rates of convergence for classes of functions: The non-i.i.d. case
• Absolute regularity and functions of Markov chains
• Empirical discrepancies and subadditive processes
• Central limit theorems for empirical measures
• Some Limit Theorems for Random Functions. I
• Some Limit Theorems for Random Functions. II
• Necessary and Sufficient Conditions for the Uniform Convergence of Means to their Expectations
• Invariance principles for sums of Banach space valued random elements and empirical processes
• Convergence of stochastic processes
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