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Nonparametric estimation of a renewal reward process from discrete data

Duval, Céline, Nonparametric estimation of a renewal reward process from discrete data, Mathematical Methods of Statistics;1066-5307, 22, 1, p. 28–56. 10.3103/S106653071301002X

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Article accepté pour publication ou publié
Nom de la revue
Mathematical Methods of Statistics;1066-5307
Volume
22
Numéro
1
Éditeur
Elsevier
Pages
28–56
Identifiant publication
Métadonnées
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Auteur(s)
Duval, Céline
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Résumé (EN)
We study the nonparametric estimation of the jump density of a renewal reward process from one discretely observed sample path over [0,T]. We consider regimes where the sampling rate goes to 0 as T tends to infinity. We propose an adaptive wavelet threshold density estimator and study its performance for the Lp loss, over Besov spaces. We achieve minimax rates of convergence for sampling rates that vanish with T at arbitrary polynomial rate. In the same spirit as Buchmann and Grübel (2003) the estimation procedure is based on the inversion of the compounding operator. The inverse has no closed form expression and is approached with a fixed point technique.
Mots-clés
wavelet density estimation; discretely observed random process; compound Poisson process; continuous time random walk; renewal reward process