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Title: Convergence rates for the strong law of large numbers under association
Authors: Henriques, Carla 
Oliveira, Paulo Eduardo 
Keywords: Association; Convergence rates; Exponential inequalities; Maximal inequalities
Issue Date: 2008
Publisher: Centro de Matemática da Universidade de Coimbra
Citation: Pré-Publicações DMUC. 08-14 (2008)
Abstract: We prove convergence rates for the Strong Laws of Large Numbers (SLLN) for associated variables which are arbitrarily close to the optimal rates for independent variables. A rst approach is based on exponential inequalities, a usual tool for this kind of problems. Following the optimization e orts of several authors, we improve the rates derived from exponential inequalities to log2 n n1=2 . A more recent approach tries to use maximal inequalities together with moment inequalities. We prove a new maximal order inequality of order 4 for associated variables, using a telescoping argument. This inequality is then used to prove a SLLN convergence rate arbitrarily close to log1=4 n n1=2 .
Rights: openAccess
Appears in Collections:FCTUC Matemática - Vários

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