Nonparametric estimation of a trend based upon sampled continuous processes

Degras, David

doi:10.1016/j.crma.2008.12.016

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]

Présenté par : Paul Deheuvels

Degras, David ¹

¹ Laboratoire de statistique théorique et appliquée, Université Paris 6, boîte 158, 175, rue du Chevaleret, 75013 Paris, France

Comptes Rendus. Mathématique, Tome 347 (2009) no. 3-4, pp. 191-194.

Résumé
Abstract

Soit X= ${X (t), t \in [0, T]}$ 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 $μ = E X$ dans l'espace $C ([0, T])$ lorsque $n, p \to \infty$ , puis nous obtenons des bandes de confiance simultanées approchées pour μ à l'aide de la théorie des processus Gaussiens.

Let $X = {X (t), t \in [0, T]}$ 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 $μ = E X$ in the space $C ([0, T])$ as $n, p \to \infty$ and, using Gaussian process theory, we derive approximate simultaneous confidence bands for μ.

Reçu le : 2008-07-19
Accepté le : 2008-12-19
Publié le : 2009-01-29

DOI : 10.1016/j.crma.2008.12.016

Affiliations des auteurs :

Degras, David ¹

¹ Laboratoire de statistique théorique et appliquée, Université Paris 6, boîte 158, 175, rue du Chevaleret, 75013 Paris, France

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     title = {Nonparametric estimation of a trend based upon sampled continuous processes},
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Degras, David. Nonparametric estimation of a trend based upon sampled continuous processes. Comptes Rendus. Mathématique, Tome 347 (2009) no. 3-4, pp. 191-194. doi : 10.1016/j.crma.2008.12.016. http://archive.numdam.org/articles/10.1016/j.crma.2008.12.016/

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