Asymptotic results for empirical and partial-sum processes: A review

DOI10.2307/3314809zbMath0574.62024OpenAlexW2052917182MaRDI QIDQ3692615

Ronald Pyke

Publication date: 1984

Published in: Canadian Journal of Statistics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2307/3314809

zbMATH Keywords

empirical processcentral limit theoremslaws of large numbersscan statisticsempirical measurepartial-sum processeslaws of iterated logarithmKolmogorov statisticsoverview of asymptotic resultsset-indexed

Mathematics Subject Classification ID

Asymptotic distribution theory in statistics (62E20) Central limit and other weak theorems (60F05) Strong limit theorems (60F15) Research exposition (monographs, survey articles) pertaining to statistics (62-02) Inference from stochastic processes (62M99) Convergence of probability measures (60B10) Research exposition (monographs, survey articles) pertaining to probability theory (60-02)

Related Items (max. 100)

Uniform strong law of large numbers ⋮ Uniform Strong Law of Large Numbers for Random Signed Measures ⋮ Lévy's Brownian motion as a set-indexed process and a related central limit theorem

Cites Work

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• A strong law of large numbers for partial-sum processes indexed by sets
• Functional law of the iterated logarithm and uniform central limit theorem for partial-sum processes indexed by sets
• Fourier analysis and determining sets for Radon measures on \({\mathbb{R}}^ n\)
• Log log laws for empirical measures
• Empirical discrepancies and subadditive processes
• Empirical processes: A survey of results for independent and identically distributed random variables
• Central limit theorems for empirical measures
• Some Strassen-type laws of the iterated logarithm for multiparameter stochastic processes with independent increments
• Sample functions of the Gaussian process
• Probability Inequalities for the Sum of Independent Random Variables
• Determination of probability measures through group actions
• Limit theorems for empirical processes
• Probability Inequalities for Sums of Bounded Random Variables
• Weak Convergence of a Two-sample Empirical Process and a New Approach to Chernoff-Savage Theorems
• The Invariance Principle for a Lattice of Random Variables
• The Law of the Iterated Logarithm for Empirical Distribution

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