Please use this identifier to cite or link to this item: http://hdl.handle.net/10316/84943
Title: ASYMPTOTIC RESULTS FOR CERTAIN WEAK DEPENDENT VARIABLES
Authors: Arab, Idir 
Oliveira, Paulo 
Keywords: Central Limit Theorem; Convergence rate; L-weak dependence; Strong law of large numbers
Issue Date: 2018
Serial title, monograph or event: Theory of Probability and Mathematical Statistics
Volume: 2
Issue: 99
Place of publication or event: Kiev
Abstract: We consider a special class of weak dependent random variables with control on covariances of Lipschitz transformations. This class includes, but is not limited to, positively, negatively associated variables and a few other classes of weakly dependent structures. We prove the Strong Law of Large Numbers with the characterization of convergence rates which is almost optimal, in the sense that it is arbitrarily close to the optimal rate for independent variables. Moreover, we prove an inequality comparing the joint distributions with the product distributions of the margins, similar to the well known Newman's inequality for characteristic functions of associated variables. As a consequence, we prove the Central Limit Theorem together with its functional counterpart, and also the convergence of the empirical process for this class of weak dependent variables.
URI: http://hdl.handle.net/10316/84943
ISSN: 0868-6904
Rights: openAccess
Appears in Collections:I&D CMUC - Artigos em Revistas Internacionais

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