The central limit theorem and the law of iterated logarithm for empirical processes under local conditions

DOI10.1007/BF00334041zbMath0618.60022OpenAlexW2083005869MaRDI QIDQ1822406

Yanyan Li

Publication date: 1988

Published in: Probability Theory and Related Fields (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00334041

zbMATH Keywords

empirical processescentral limit theoremlaw of iterated logarithm

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Functional limit theorems; invariance principles (60F17)

Related Items

Concentration inequalities, large and moderate deviations for self-normalized empirical processes, Weak convergence of some classes of martingales with jumps., Rates of convergence for minimum contrast estimators, Bootstraps of sums of independent but not identically distributed stochastic processes, The central limit theorem for empirical processes on V-Č classes: A majorizing measure approach, Kaplan-Meier estimators of distance distributions for spatial point processes, Bracketing metric entropy rates and empirical central limit theorems for function classes of Besov- and Sobolev-type, Laws of the iterated logarithm for partial sum processes indexed by functions, Limit Theorems for Quantile and Depth Regions for Stochastic Processes, Weak convergence for the row sums of a triangular array of empirical processes under bracketing conditions, A CLT for weighted time-dependent uniform empirical processes, Equivalent processes of total time on test, Lorenz and inverse Lorenz processes, Bootstrapping sums of independent but not identically distributed continuous processes with applications to functional data, A Donsker-type theorem for log-likelihood processes, The Central Limit Theorem for Empirical Processes Under Local Conditions: The Case of Radon Infinitely Divisible Limits without Gaussian Component, Consistent specification tests for semiparametric/nonparametric models based on series estimation methods

Cites Work

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• Central limit theorems for C(S)-valued random variables
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• Some stability results for vector valued random variables
• Central limit theorems for empirical measures
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• Probability Inequalities for the Sum of Independent Random Variables
• Invariance principles for sums of Banach space valued random elements and empirical processes
• [https://portal.mardi4nfdi.de/wiki/Publication:3956139 Loi du logarithme it�r� dans C S) et fonction caract�ristique empirique]
• [https://portal.mardi4nfdi.de/wiki/Publication:4104649 Mesures majorantes et th�or�me de la limite centrale dans C(S)]
• [https://portal.mardi4nfdi.de/wiki/Publication:4181018 Relation entre th�or�me central-limite et loi du logarithme it�r� dans les espaces de Banach]
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