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Theses
APPLICATIONS STATISTIQUES DE SUITES FAIBLEMENT DEPENDANTES ET DE SYSTEMES DYNAMIQUES
Abstract : This thesis deals with the study
of some statical applications of dependent and stationary
sequences. We study two classes of dependent sequences : weak
dependent sequences in a sense which is a variation on the notion
introduced by Doukhan \& Louhichi, and some dynamical
systems whose correlations decrease. We study the asymptotical behaviour
of the empirical process, which is very important in statistics. We
also study standard kernel density estimates in both frames. We
finally investigate a change point estimator of some regression
function in our frame of weak dependence. The main tool to study these
applications is a variation on Rio's ideas to prove a
Central Limit Theorem for weakly dependent sequences as far as some
new moment inequalities which extend Louhichi's inequalities. We also make some numerical simulations concerning some of our resul
ts.
of some statical applications of dependent and stationary
sequences. We study two classes of dependent sequences : weak
dependent sequences in a sense which is a variation on the notion
introduced by Doukhan \& Louhichi, and some dynamical
systems whose correlations decrease. We study the asymptotical behaviour
of the empirical process, which is very important in statistics. We
also study standard kernel density estimates in both frames. We
finally investigate a change point estimator of some regression
function in our frame of weak dependence. The main tool to study these
applications is a variation on Rio's ideas to prove a
Central Limit Theorem for weakly dependent sequences as far as some
new moment inequalities which extend Louhichi's inequalities. We also make some numerical simulations concerning some of our resul
ts.
Mots-clés :
fonction de régression Dépendance faible suites
stationnaires systèmes dynamiques décroissance des
corrélations théorème limite centrale théorème de Lindeberg densité invariante estimation non-paramétrique
estimation à noyau inégalités de moments processus empirique
loi forte des grands nombres de Marcinkiewicz-Zygmund rupture
fonction de régression.
fonction de régression Dépendance faible suites
stationnaires systèmes dynamiques décroissance des
corrélations théorème limite centrale théorème de Lindeberg densité invariante estimation non-paramétrique
estimation à noyau inégalités de moments processus empirique
loi forte des grands nombres de Marcinkiewicz-Zygmund rupture
fonction de régression.
Cited literature [34 references]
https://tel.archives-ouvertes.fr/tel-00001436
Contributor : Clementine Prieur <>
Submitted on : Thursday, June 20, 2002 - 3:24:27 PM
Last modification on : Thursday, March 5, 2020 - 12:06:06 PM
Long-term archiving on: : Tuesday, September 11, 2012 - 5:36:03 PM
Contributor : Clementine Prieur <>
Submitted on : Thursday, June 20, 2002 - 3:24:27 PM
Last modification on : Thursday, March 5, 2020 - 12:06:06 PM
Long-term archiving on: : Tuesday, September 11, 2012 - 5:36:03 PM