Adaptive estimation of the conditional intensity of marker-dependent counting processes

F. Comte; S. Gaïffas; A. Guilloux

Annales de l'I.H.P. Probabilités et statistiques (2011)

  • Volume: 47, Issue: 4, page 1171-1196
  • ISSN: 0246-0203

Abstract

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We propose in this work an original estimator of the conditional intensity of a marker-dependent counting process, that is, a counting process with covariates. We use model selection methods and provide a nonasymptotic bound for the risk of our estimator on a compact set. We show that our estimator reaches automatically a convergence rate over a functional class with a given (unknown) anisotropic regularity. Then, we prove a lower bound which establishes that this rate is optimal. Lastly, we provide a short illustration of the way the estimator works in the context of conditional hazard estimation.

How to cite

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Comte, F., Gaïffas, S., and Guilloux, A.. "Adaptive estimation of the conditional intensity of marker-dependent counting processes." Annales de l'I.H.P. Probabilités et statistiques 47.4 (2011): 1171-1196. <http://eudml.org/doc/243314>.

@article{Comte2011,
abstract = {We propose in this work an original estimator of the conditional intensity of a marker-dependent counting process, that is, a counting process with covariates. We use model selection methods and provide a nonasymptotic bound for the risk of our estimator on a compact set. We show that our estimator reaches automatically a convergence rate over a functional class with a given (unknown) anisotropic regularity. Then, we prove a lower bound which establishes that this rate is optimal. Lastly, we provide a short illustration of the way the estimator works in the context of conditional hazard estimation.},
author = {Comte, F., Gaïffas, S., Guilloux, A.},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {marker-dependent counting process; conditional intensity; model selection; adaptive estimation; minimax and nonparametric methods; censored data; conditional hazard function},
language = {eng},
number = {4},
pages = {1171-1196},
publisher = {Gauthier-Villars},
title = {Adaptive estimation of the conditional intensity of marker-dependent counting processes},
url = {http://eudml.org/doc/243314},
volume = {47},
year = {2011},
}

TY - JOUR
AU - Comte, F.
AU - Gaïffas, S.
AU - Guilloux, A.
TI - Adaptive estimation of the conditional intensity of marker-dependent counting processes
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2011
PB - Gauthier-Villars
VL - 47
IS - 4
SP - 1171
EP - 1196
AB - We propose in this work an original estimator of the conditional intensity of a marker-dependent counting process, that is, a counting process with covariates. We use model selection methods and provide a nonasymptotic bound for the risk of our estimator on a compact set. We show that our estimator reaches automatically a convergence rate over a functional class with a given (unknown) anisotropic regularity. Then, we prove a lower bound which establishes that this rate is optimal. Lastly, we provide a short illustration of the way the estimator works in the context of conditional hazard estimation.
LA - eng
KW - marker-dependent counting process; conditional intensity; model selection; adaptive estimation; minimax and nonparametric methods; censored data; conditional hazard function
UR - http://eudml.org/doc/243314
ER -

References

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