no. 10
Statistics/Probability Theory
Almost sure convergence of the kT-occupation time density estimator
[Convergence presque sûre de l'estimateur de la densité du kT-temps d'occupation]

Présenté par : Paul Deheuvels

Labrador, Boris1
1 L.S.T.A., université Paris 6, 175, rue du Chevaleret, 75013 Paris, France
Comptes Rendus. Mathématique, Tome 343 (2006) no. 10, pp. 665-669.

Dans cette Note, nous introduisons une extension de l'estimateur des k-plus proches voisins en temps continu, l'estimateur du kT-temps d'occupation, puis nous donnons des conditions d'existence de cet estimateur. Nous établissons également la convergence presque sûre pour des processus bornés α-mélangeants dans deux cas, le cas suroptimal (où la vitesse paramétrique est atteinte) et le cas optimal (où la vitesse i.i.d. de l'estimation de la densité est atteinte).

In this Note, we introduce an extension of the k-nearest neighbor estimator in continuous time, the kT-occupation time estimator, and we give sufficient conditions for its existence. Then, we show the almost sure convergence for α-mixing and bounded processes in two cases, the superoptimal case (when parametric rates are reached) and the optimal case (when i.i.d. rates of density estimation are reached).

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2006.10.015
Labrador, Boris 1

1 L.S.T.A., université Paris 6, 175, rue du Chevaleret, 75013 Paris, France 
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Labrador, Boris. Almost sure convergence of the $ {k}_{T}$-occupation time density estimator. Comptes Rendus. Mathématique, Tome 343 (2006) no. 10, pp. 665-669. doi : 10.1016/j.crma.2006.10.015. http://www.numdam.org/articles/10.1016/j.crma.2006.10.015/

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