A new covariance inequality and applications

被引：75

作者：

Dedecker, J

Doukhan, P

机构：

[1] Univ Paris 06, Lab Stat Theoret & Appl, F-75013 Paris, France

[2] Univ Cergy Pontoise, LS CREST, Cergy, France

[3] Univ Cergy Pontoise, UMR 8088, Cergy, France

来源：

STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 2003年 / 106卷 / 01期

关键词：

weak dependence; mixingales; strong mixing; covariance inequalities; weak invariance principle; moment inequalities;

D O I：

10.1016/S0304-4149(03)00040-1

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We compare three dependence coefficients expressed in terms of conditional expectations, and we study their behaviour in various situations. Next, we give a new covariance inequality involving the weakest of those coefficients, and we compare this bound to that obtained by Rio (Ann. Inst. H. Poincare Probab. Statist. 29 (1993) 587-597) in the strongly mixing case. This new inequality is used to derive sharp limit theorems, such as Donsker's invariance principle and Marcinkiewicz's strong law. As a consequence of a Burkholder-type inequality, we obtain a deviation inequality for partial sums. (C) 2003 Elsevier Science B.V. All rights reserved.

引用

页码：63 / 80

页数：18

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