Rates of uniform convergence of empirical means with mixing processes

DOI10.1016/S0167-7152(02)00124-4zbMath1016.60036OpenAlexW2002196465MaRDI QIDQ1871232

Rajeeva L. Karandikar, Mathukumalli Vidyasagar

Publication date: 7 May 2003

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

Full work available at URL: https://doi.org/10.1016/s0167-7152(02)00124-4

zbMATH Keywords

uniform convergence\(\beta\)-mixingstationary sequence

Mathematics Subject Classification ID

Time series, auto-correlation, regression, etc. in statistics (GARCH) (62M10) Stationary stochastic processes (60G10) Convergence of probability measures (60B10) Functional limit theorems; invariance principles (60F17)

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Cites Work

• The Glivenko-Cantelli problem
• Decision theoretic generalizations of the PAC model for neural net and other learning applications
• Subadditive ergodic theory
• Empirical discrepancies and subadditive processes
• Rates of convergence for empirical processes of stationary mixing sequences
• A note on uniform laws of averages for dependent processes
• Weak convergence and empirical processes. With applications to statistics
• Fat-shattering and the learnability of real-valued functions
• Necessary and Sufficient Conditions for the Uniform Convergence of Means to their Expectations
• Scale-sensitive dimensions, uniform convergence, and learnability
• On the Uniform Convergence of Relative Frequencies of Events to Their Probabilities
• Convergence of stochastic processes
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