Comptes Rendus
Statistics
Nonparametric estimation of a trend based upon sampled continuous processes
[Estimation non paramétrique d'une tendance à partir de réalisations d'un processus à temps continu]
Comptes Rendus. Mathématique, Volume 347 (2009) no. 3-4, pp. 191-194.

Soit X={X(t),t[0,T]} un processus aléatoire du second ordre dont on observe n réalisations indépendantes sur une grille de p points déterministes. Sous de faibles conditions de régularité sur les trajectoires de X, nous prouvons la normalité asymptotique d'estimateurs non paramétriques de la tendance μ=EX dans l'espace C([0,T]) lorsque n,p, puis nous obtenons des bandes de confiance simultanées approchées pour μ à l'aide de la théorie des processus Gaussiens.

Let X={X(t),t[0,T]} be a second order random process of which n independent realizations are observed on a fixed grid of p time points. Under mild regularity assumptions on the sample paths of X, we show the asymptotic normality of suitable nonparametric estimators of the trend function μ=EX in the space C([0,T]) as n,p and, using Gaussian process theory, we derive approximate simultaneous confidence bands for μ.

Reçu le :
Accepté le :
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DOI : 10.1016/j.crma.2008.12.016

David Degras 1

1 Laboratoire de statistique théorique et appliquée, Université Paris 6, boîte 158, 175, rue du Chevaleret, 75013 Paris, France
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David Degras. Nonparametric estimation of a trend based upon sampled continuous processes. Comptes Rendus. Mathématique, Volume 347 (2009) no. 3-4, pp. 191-194. doi : 10.1016/j.crma.2008.12.016. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2008.12.016/

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