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Comptes Rendus Mathématique
Volume 341, n° 1
pages 59-62 (juillet 2005)
Doi : 10.1016/j.crma.2005.05.003
Received : 30 January 2005 ;  accepted : 13 May 2005
Vitesses optimale et suroptimale des polygones de fréquences pour les processus à temps continu
Optimal and superoptimal rates of frequency polygons for continuous-time processes

François-Xavier Lejeune
LSTA, université Paris 6, 175, rue du Chevaleret, 75013 Paris, France 


Cette Note porte sur les vitesses de convergence dʼun estimateur non-paramétrique de la densité dʼun processus à temps continu. Plus précisément, sous certaines hypothèses de régularité et dʼindépendance asymptotique, lʼerreur quadratique intégrée du polygone de fréquences converge vers zéro à la vitesse optimale   du cas i.i.d. Avec une condition locale plus faible que celle de Castellana-Leadbetter [Stochastic Process. Appl. 21 (1986) 179-193], la vitesse « suroptimale »   est obtenue. Pour citer cet article : F.-X. Lejeune, C. R. Acad. Sci. Paris, Ser. I 341 (2005).

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This Note deals with density estimation in continuous-time. Then under mild regularity and asymptotic independence conditions, the mean integrated square error achieves the same optimal rate   of convergence to zero as in the i.i.d. case. Under a local assumption weaker than Castellana-Leadbetterʼs [Stochastic Process. Appl. 21 (1986) 179-193], we obtain the parametric rate  . To cite this article: F.-X. Lejeune, C. R. Acad. Sci. Paris, Ser. I 341 (2005).

The full text of this article is available in PDF format.

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