Nonparametric estimation of the jump rate for non-homogeneous marked renewal processes

Romain Azaïs; François Dufour; Anne Gégout-Petit

Annales de l'I.H.P. Probabilités et statistiques (2013)

  • Volume: 49, Issue: 4, page 1204-1231
  • ISSN: 0246-0203

Abstract

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This paper is devoted to the nonparametric estimation of the jump rate and the cumulative rate for a general class of non-homogeneous marked renewal processes, defined on a separable metric space. In our framework, the estimation needs only one observation of the process within a long time. Our approach is based on a generalization of the multiplicative intensity model, introduced by Aalen in the seventies. We provide consistent estimators of these two functions, under some assumptions related to the ergodicity of an embedded chain and the characteristics of the process. The paper is illustrated by a numerical example.

How to cite

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Azaïs, Romain, Dufour, François, and Gégout-Petit, Anne. "Nonparametric estimation of the jump rate for non-homogeneous marked renewal processes." Annales de l'I.H.P. Probabilités et statistiques 49.4 (2013): 1204-1231. <http://eudml.org/doc/272081>.

@article{Azaïs2013,
abstract = {This paper is devoted to the nonparametric estimation of the jump rate and the cumulative rate for a general class of non-homogeneous marked renewal processes, defined on a separable metric space. In our framework, the estimation needs only one observation of the process within a long time. Our approach is based on a generalization of the multiplicative intensity model, introduced by Aalen in the seventies. We provide consistent estimators of these two functions, under some assumptions related to the ergodicity of an embedded chain and the characteristics of the process. The paper is illustrated by a numerical example.},
author = {Azaïs, Romain, Dufour, François, Gégout-Petit, Anne},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {non-homogeneous marked renewal process; nonparametric estimation; jump rate estimation; Nelson–Aalen estimator; asymptotic consistency; ergodicity of Markov chains; Nelson-Aalen estimator},
language = {eng},
number = {4},
pages = {1204-1231},
publisher = {Gauthier-Villars},
title = {Nonparametric estimation of the jump rate for non-homogeneous marked renewal processes},
url = {http://eudml.org/doc/272081},
volume = {49},
year = {2013},
}

TY - JOUR
AU - Azaïs, Romain
AU - Dufour, François
AU - Gégout-Petit, Anne
TI - Nonparametric estimation of the jump rate for non-homogeneous marked renewal processes
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2013
PB - Gauthier-Villars
VL - 49
IS - 4
SP - 1204
EP - 1231
AB - This paper is devoted to the nonparametric estimation of the jump rate and the cumulative rate for a general class of non-homogeneous marked renewal processes, defined on a separable metric space. In our framework, the estimation needs only one observation of the process within a long time. Our approach is based on a generalization of the multiplicative intensity model, introduced by Aalen in the seventies. We provide consistent estimators of these two functions, under some assumptions related to the ergodicity of an embedded chain and the characteristics of the process. The paper is illustrated by a numerical example.
LA - eng
KW - non-homogeneous marked renewal process; nonparametric estimation; jump rate estimation; Nelson–Aalen estimator; asymptotic consistency; ergodicity of Markov chains; Nelson-Aalen estimator
UR - http://eudml.org/doc/272081
ER -

References

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