The Hájek-Rènyi inequality and strong law of large numbers for ANA random variables

DOI10.1186/1029-242X-2014-521zbMath1372.60021OpenAlexW2129580044WikidataQ59320235 ScholiaQ59320235MaRDI QIDQ2405766

Mi-Hwa Ko

Publication date: 26 September 2017

Published in: Journal of Inequalities and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1186/1029-242x-2014-521

zbMATH Keywords

complete convergenceMarcinkiewicz strong law of large numbersasymptotically negative associationHájek-Rènyi inequality

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Strong limit theorems (60F15)

Related Items (5)

The central limit theorem for ANA sequences and its application to nonparametric regression models ⋮ Some strong convergence properties for arrays of rowwise ANA random variables ⋮ SOME LIMITING BEHAVIOR FOR ASYMPTOTICALLY NEGATIVE ASSOCIATED RANDOM VARIABLES ⋮ Complete convergence and complete moment convergence for arrays of rowwise ANA random variables ⋮ Complete moment convergence for weighted sums of m-asymptotic negatively associated random variables

Cites Work

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• Limiting behavior of the maximum of the partial sum for asymptotically negatively associated random variables under residual Cesáro alpha-integrability assumption
• The Hájek-Rényi inequality for the NA random variables and its application
• The Hájek-Rényi inequality for Banach space valued martingales and the \(p\) smoothness of Banach spaces
• On the strong law for asymptotically almost negatively associated random variables
• Negative association of random variables, with applications
• Inequalities of maximum of partial sums and weak convergence for a class of weak dependent random variables
• Generalization of an inequality of Kolmogorov
• A Martingale Inequality and the Law of Large Numbers
• Central limit theorems for asymptotically negatively associated random fields
• A functional central limit theorem for asymptotically negatively dependent random fields

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