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Titre :
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Nonparametric estimation for renewal and Markov processes
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Auteurs :
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O. Pons, Auteur
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Type de document :
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ouvrage
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Editeur :
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Paris [FRA] : Lavoisier, 2009
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ISBN/ISSN/EAN :
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978-2-9534122-1-5
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Format :
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262 p. / couv. ill. en coul. / 24 cm
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Langues:
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= Anglais
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Mots-clés:
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NON-PARAMETRIC
;
MARKOV
;
RENEWAL
;
STATISTIQUES
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Résumé :
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The aim of the book is the nonparametric estimation of models for the distribution of marked point processes. The observation of the sample-paths is partial due to left or right censoring or truncation. Nonparametric Estimation for Renewal and Markov Processes presents nonparametric estimators for the distribution of variables and the associated hazard functions. The methods are generalized to the nonparametric regression and to inhomogeneous renewal or Markov processes. The asymptotic behavior of new functional estimators is studied under various conditions about the observed sample-paths and the ergodicity is established in several cases. For left censored or truncated variables and sample-paths, a reverse martingale related to the point process of the observed events provides simple results for the classical estimator and its extensions. Mixtures of point processes and auto-regressive processes are also considered. The book is intended to researchers, teachers and students in mathematical statistics and interested in the application of statistical methods. Backgrounds in probability and statistics
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