Comptes Rendus
no. 7
Probabilités/Statistique
Inégalités de covariance
[Covariance inequalities.]

Presented by: Paul Deheuvels

Jérôme Dedecker1
1 Laboratoire de statistique théorique et appliquée, université Paris 6, site Chevaleret, 13, rue Clisson, 75013 Paris, France
Comptes Rendus. Mathématique, Volume 339 (2004) no. 7, pp. 503-506.

In this Note, we show that some well known covariance inequalities expressed in terms of mixing coefficients remain true for weaker coefficients. Next, we give some examples of non-mixing processes for which these weaker coefficients can be easily bounded.

Dans cette Note, nous montrons que certaines inégalités de covariance écrites en terme de coefficients de mélange restent vraies pour des versions faibles de ces coefficients. Nous donnons ensuite quelques exemples de processus non-mélangeants pour lesquels nous pouvons obtenir sans peine des bornes pour les coefficients faibles.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2004.09.005

Jérôme Dedecker 1

1 Laboratoire de statistique théorique et appliquée, université Paris 6, site Chevaleret, 13, rue Clisson, 75013 Paris, France 
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Jérôme Dedecker. Inégalités de covariance. Comptes Rendus. Mathématique, Volume 339 (2004) no. 7, pp. 503-506. doi : 10.1016/j.crma.2004.09.005. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2004.09.005/

[1] R.C. Bradley Basic properties of strong mixing conditions (E. Eberlein; M.S. Taquu, eds.), Dependence in Probability and Statistics. A Survey of Recent Results, Oberwolfach, 1985, Birkhäuser, 1986, pp. 165-192

[2] J. Dedecker, C. Prieur, New dependence coefficients. Examples and applications to statistics, Prépublication, 2003. http:www.ccr.jussieu.fr/lsta/prepublications.html

[3] B. Delyon, Limit theorems for mixing processes, Tech. Report 546 IRISA, Rennes I, 1990

[4] M. Peligrad A note on two measures of dependence and mixing sequences, Adv. Appl. Probab., Volume 15 (1983), pp. 461-464

[5] T.D. Phan; L.T. Tran Some mixing properties of time series models, Stochastic Process. Appl., Volume 19 (1985), pp. 297-303

[6] G. Viennet Inequalities for absolutely regular sequences: application to density estimation, Probab. Theory Related Fields, Volume 107 (1997), pp. 467-492

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