A weak convergence for negatively associated fields

DOI10.1016/S0167-7152(01)00021-9zbMath0994.60026OpenAlexW1995783103MaRDI QIDQ5952092

Ji-Wei Wen, Zhang, Lixin

Publication date: 7 October 2002

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

Full work available at URL: https://doi.org/10.1016/s0167-7152(01)00021-9

zbMATH Keywords

weak convergencerandom fieldnegative associationmaximal inequalities

Mathematics Subject Classification ID

Random fields (60G60) Asymptotic distribution theory in statistics (62E20) Central limit and other weak theorems (60F05)

Related Items (20)

Determinantal probability measures ⋮ Rosenthal's inequalities for independent and negatively dependent random variables under sub-linear expectations with applications ⋮ Maximal moment inequality for partial sums of strong mixing sequences and application ⋮ On Complete Convergence for Weighted Sums of NA Random Fields ⋮ The strong law of large numbers for linear random fields generated by negatively associated random variables on \(Z^d\) ⋮ Some laws of large numbers for arrays of random upper semicontinuous functions ⋮ On tail triviality of negatively dependent stochastic processes ⋮ Convergence rates in the strong laws for a class of dependent random fields ⋮ Estimation of partial linear error-in-variables models for \(\rho ^{ - }\)-mixing dependence data ⋮ Stationary determinantal processes: phase multiplicity, Bernoullicity, entropy, and domination ⋮ A note on the almost sure central limit theorem for negatively associated fields ⋮ A strong invariance principle for negatively associated random fields ⋮ Central limit theorems for asymptotically negatively associated random fields ⋮ Convergence rates in the SLLN for some classes of dependent random fields ⋮ Moment inequalities and convergence rates in the strong laws for \(\rho^-\)-mixing random fields ⋮ A General Multiparameter Version of Gnedenko's Transfer Theorem ⋮ Moment inequality and complete convergence of moving average processes under asymptotically linear negative quadrant dependence assumptions ⋮ Inequalities of maximum of partial sums and weak convergence for a class of weak dependent random variables ⋮ Uniform bounds in normal approximation under negatively associated random fields ⋮ Convergence rates in the law of the iterated logarithm for negatively associated random variables with multidimensional indices

Cites Work

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• An invariance principle for certain dependent sequences
• A note on the almost sure convergence of sums of negatively dependent random variables
• Rosenthal type inequalities for \(B\)-valued strong mixing random fields and their applications
• Asymptotic normality of random fields of positively or negatively associated processes
• Moment inequalities and weak convergence for negatively associated sequences
• A comparison theorem on moment inequalities between negatively associated and independent random variables
• The law of iterated logarithm for negatively associated random variables
• Negative association of random variables, with applications
• Convergence rates in the strong laws of asymptotically negatively associated random fields
• Maximum of partial sums and an invariance principle for a class of weak dependent random variables
• A functional central limit theorem for asymptotically negatively dependent random fields

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