Asymptotic results for empirical measures of weighted sums of independent random variables

2 CQFD - Quality control and dynamic reliability
IMB - Institut de Mathématiques de Bordeaux, Inria Bordeaux - Sud-Ouest
Abstract : We prove that if a rectangular matrix with uniformly small entries and approximately orthogonal rows is applied to the independent standardized random variables with uniformly bounded third moments, then the empirical CDF of the resulting partial sums converges to the normal CDF with probability one. This implies almost sure convergence of empirical periodograms, almost sure convergence of spectra of circulant and reverse circulant matrices, and almost sure convergence of the CDF's generated from independent random variables by independent random orthogonal matrices. For special trigonometric matrices, the speed of the almost sure convergence is described by the normal approximation and by the large deviation principle.
Type de document :
Article dans une revue
Electronic Communications in Probability, Institute of Mathematical Statistics (IMS), 2006, 12, pp.184-199
Domaine :

https://hal.archives-ouvertes.fr/hal-00339764
Contributeur : Bernard Bercu <>
Soumis le : mardi 18 novembre 2008 - 18:07:52
Dernière modification le : mercredi 28 février 2018 - 10:22:49

Citation

Bernard Bercu, Wlodzimierz Bryc. Asymptotic results for empirical measures of weighted sums of independent random variables. Electronic Communications in Probability, Institute of Mathematical Statistics (IMS), 2006, 12, pp.184-199. 〈hal-00339764〉

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