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Nonparametric estimation of a renewal reward process from discrete data

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Dewey
Probabilités et mathématiques appliquées
Sujet
wavelet density estimation; discretely observed random process; compound Poisson process; continuous time random walk; renewal reward process
Journal issue
Mathematical Methods of Statistics;1066-5307
Volume
22
Number
1
Publication date
01-2013
Article pages
28–56
Publisher
Elsevier
DOI
http://dx.doi.org/10.3103/S106653071301002X
URI
https://basepub.dauphine.fr/handle/123456789/17426
Collections
  • CEREMADE : Publications
Metadata
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Author
Duval, Céline
60 CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Type
Article accepté pour publication ou publié
Abstract (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.

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