Laws of large numbers for Cesàro alpha-integrable random variables under dependence condition AANA or AQSI

DOI10.1007/S10114-012-0033-3zbMath1252.60031OpenAlexW1149415584MaRDI QIDQ1757977

Jun An, De-Mei Yuan

Publication date: 7 November 2012

Published in: Acta Mathematica Sinica. English Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10114-012-0033-3

zbMATH Keywords

law of large numbersresidual Cesàro alpha-integrabilityasymptotically almost negative associationasymptotically quadrant sub-independencestrong residual Cesàro alpha-integrability

Mathematics Subject Classification ID

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

Related Items (13)

Hájek-Rényi inequality for \(m\)-asymptotically almost negatively associated random vectors in Hilbert space and applications ⋮ On complete moment convergence for CAANA random vectors in Hilbert spaces ⋮ Further study on complete convergence for weighted sums of arrays of rowwise asymptotically almost negatively associated random variables ⋮ L^p convergence and complete convergence for weighted sums of AANA random variables ⋮ Complete convergence and complete moment convergence for arrays of rowwise asymptotically almost negatively associated random variables ⋮ Some conditional results for conditionally strong mixing sequences of random variables ⋮ Some strong laws of large numbers, L₂-convergence and complete convergence for m-AANA random vectors in Hilbert space ⋮ Some strong laws of large numbers for weighted sums of asymptotically almost negatively associated random variables ⋮ On consistency of the weighted estimator in nonparametric regression model with asymptotically almost negatively associated random variables ⋮ On consistency of the nearest neighbor estimator of the density function and its applications ⋮ On complete consistency for the estimator of nonparametric regression model based on asymptotically almost negatively associated errors ⋮ Unnamed Item ⋮ Strong convergence for sequences of asymptotically almost negatively associated random variables

Cites Work

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• Rosenthal type inequalities for asymptotically almost negatively associated random variables and applications
• On dominations between measures of dependence
• Laws of large numbers under dependence assumptions
• A note on the almost sure convergence of sums of negatively dependent random variables
• Cesàro \({\alpha}\)-integrability and laws of large numbers. I
• Extensions of the strong law of large numbers of Marcinkiewicz and Zygmund for dependent variables
• The strong law of large numbers for weighted averages under dependence assumptions
• Laws of Large Numbers for Pairwise Independent Uniformly Integrable Random Variables
• Some Concepts of Dependence

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