Centre for Mathematics, University of Coimbra

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Type:	Preprint
National /International:	International
Title:	Asymptotic results for certain weak dependent variables
Publication Date:	2016-01-11
Authors:	- Idir Arab - Paulo Eduardo Oliveira
Abstract:	We consider a special class of weak dependent random variables with control on covariances of Lipschitz transformations. This class includes positively, negatively associated variables and a few other classes of weakly dependent structures. We prove a Strong Law of Large Numbers with a 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 inequality for characteristic functions of associated variables. As a consequence, we prove a Central Limit Theorem, together with its functional counterpart, and also the convergence of the empirical process for this class of weak dependent variables.
Institution:	DMUC 16-01
Online version:	http://www.mat.uc.pt...prints/eng_2016.html
Download:	Not available