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Mme AFROUN F\u00efrouz<\/span><\/strong>.<\/span><\/p>\n Soutiendra sa th\u00e9se de doctorat en Math\u00e9matiques Sp\u00e9cialit\u00e9: Recherche Op\u00e9rationnelle et Optimisation.<\/span><\/p>\n Intitul\u00e9 \u00ab<\/strong>Estimation non param\u00e9trique dans les processus Markoviens<\/span>\u00bb<\/strong>.<\/span><\/p>\n <\/strong>Le\u00a0: 15 Mars 2022 <\/span><\/strong>\u00e0 la salle de visioconf\u00e9rences du Centre des Syst\u00e8mes et R\u00e9seaux de l\u2019Universit\u00e9\u00a0 Mouloud Mammeri de Tizi-Ouzou \u00e0 09h :30<\/span>.<\/strong><\/span><\/p>\n <\/strong><\/span><\/p>\n Devant le jury compos\u00e9 de :<\/strong><\/span><\/p>\n <\/strong><\/p>\n <\/strong><\/span><\/p>\n R\u00e9sum\u00e9:<\/strong><\/span><\/p>\n L’objet de cette th\u00e8se est d’analyser l’influence du couple (param\u00e8tre de lissage, noyau) sur les estimations des caract\u00e9ristiques d’une cha\u00eene de Markov (mod\u00e9lisant un syst\u00e8me de file d’attente) lorsque l’une des lois g\u00e9n\u00e9rales qui la r\u00e9git est enti\u00e8rement inconnue et\u00a0 remplac\u00e9e par son estimateur \u00e0 noyau.\u00a0 En effet, les \u00e9tudes de simulation men\u00e9es dans ce cadre ont mis en \u00e9vidence les limites des m\u00e9thodes d’estimation param\u00e9triques dans les cha\u00eenes de Markov. Ainsi, les r\u00e9sultats obtenus dans l’analyse des propri\u00e9t\u00e9s statistiques (biais, variance, MSE, distribution) des mesures de performance de la cha\u00eene de Markov bidimensionnelle, d\u00e9crivant le syst\u00e8me d’attente M\/M\/1\/C (avec vacances multiples, Bernoulli feedback, balking,\u00a0 reneging et\u00a0 r\u00e9tention des clients impatients et possibilit\u00e9 de panne et r\u00e9paration du serveur) montrent que la qualit\u00e9 des\u00a0 estimations de ces mesures d\u00e9pend du param\u00e8tre de d\u00e9part estim\u00e9 et que des \u00e9chantillons de grande taille sont\u00a0 n\u00e9cessaires pour obtenir des estimations d’une qualit\u00e9 raisonnable. D’autre part, ces \u00e9tudes de simulation ont \u00e9galement mis en\u00a0 \u00e9vidence l’int\u00e9r\u00eat de la s\u00e9lection\u00a0 du param\u00e8tre de lissage par les m\u00e9thodes bas\u00e9es sur la minimisation\u00a0\u00a0 des normes matricielles ainsi que le\u00a0 choix minutieux du noyau dans la construction de l’estimateur \u00e0 noyau des matrices de transition associ\u00e9es aux\u00a0 cha\u00eenes de Markov discr\u00e8tes (d\u00e9crivant les deux files d’attente D \/ G \/ 1 \/ C et\u00a0 GI \/ D \/ 1 \/ C ). \u00a0En effet, nos r\u00e9sultats indiquent qu’il est plus judicieux de s\u00e9lectionner le param\u00e8tre de lissage en minimisant\u00a0 les normes matricielles, en particulier la norme ||. ||2<\/sub> combin\u00e9e avec le noyau triangulaire, et \u00e9viter l’utilisation du noyau binomial n\u00e9gatif.<\/span><\/p>\n Mots cl\u00e9s<\/strong>: Estimation; Cha\u00eenes de Markov; Files d’attente; Mesures de performance; Param\u00e8tre de lissage; Noyaux discrets; Simulation.<\/span><\/p>\n ABSTRACT:<\/strong><\/span><\/p>\n The object of this thesis was to analyze the influence of the couple (smoothing parameter, kernel) on the estimates of Markov chain characteristics when one of the general laws governing it is entirely unknown and replaced by its kernel estimator. The simulation studies carried out in this framework, on the one hand, have highlighted the limits of parametric estimation methods in Markov chains where the results obtained in the analysis of statistical properties (bias, variance, MSE, distribution ) of the performance measures of the two-dimensional Markov chain, describing the\u00a0 M \/ M \/ 1 \/ C\u00a0 queue with multiple vacations, Bernoulli feedback, balking, reneging and retention of impatient customers and the possibility of server failure and repair, show that the quality of the estimates of these measures depends on the estimated starting parameter and that large-sizes sample are necessary to obtain estimates of reasonable quality. On the other hand, the interest of the selection of the smoothing parameter by the methods based on the minimization of the matrix norms as well as the judicious choice of the kernel in the construction of the kernel estimator of the transition matrices associated with the discrete-times Markov chains describing the two D \/ G \/ 1 \/ C and GI \/ D \/ 1 \/ C queues. Indeed, our results indicate that it is more preferable to select the smoothing parameter by minimizing the matrix norms, in particular, the norm ||. ||2<\/sub> combined with the triangular kernel, and avoids the use of the negative binomial kernel.<\/span><\/p>\n \u00a0Key words<\/strong> : Estimation; Markov chains; Queues; Performance measures; Smoothing parameter; Discrete kernels; Simulation.<\/span><\/p>\n \u00a0<\/span><\/p>\n [\/et_pb_text][\/et_pb_column][\/et_pb_row][\/et_pb_section]<\/p>\n","protected":false},"excerpt":{"rendered":" Mme AFROUN F\u00efrouz. Soutiendra sa th\u00e9se de doctorat en Math\u00e9matiques Sp\u00e9cialit\u00e9: Recherche Op\u00e9rationnelle et Optimisation. Intitul\u00e9 \u00abEstimation non param\u00e9trique dans les processus Markoviens\u00bb. Le\u00a0: 15 Mars 2022 \u00e0 la salle de visioconf\u00e9rences du Centre des Syst\u00e8mes et R\u00e9seaux de l\u2019Universit\u00e9\u00a0 Mouloud Mammeri de Tizi-Ouzou \u00e0 09h :30. Devant le jury compos\u00e9 de : Mr Aidene […]<\/p>\n","protected":false},"author":13,"featured_media":132,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_et_pb_use_builder":"on","_et_pb_old_content":"","_et_gb_content_width":"","footnotes":""},"categories":[1],"tags":[],"class_list":["post-11659","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-non-classe"],"yoast_head":"\n\n\n
\n Mr Aidene Mohammed<\/strong><\/td>\n Professeur<\/strong><\/td>\n UMMTO<\/strong><\/td>\n Pr\u00e9sident<\/strong><\/td>\n<\/tr>\n \n Mr A\u00efssani Djamil<\/strong><\/td>\n Professeur<\/strong><\/td>\n U. B\u00e9jaia<\/strong><\/td>\n Rapporteur<\/strong><\/td>\n<\/tr>\n \n Mr Hamadouche Djamel<\/strong><\/td>\n Professeur<\/strong><\/td>\n UMMTO<\/strong><\/td>\n Co-Rapporteur<\/strong><\/td>\n<\/tr>\n \n Mr Fellag Hocine<\/strong><\/td>\n Professeur<\/strong><\/td>\n USTHB<\/strong><\/td>\n Examinateur<\/strong><\/td>\n<\/tr>\n \n Mr Adjabi Sma\u00efl<\/strong><\/td>\n Professeur<\/strong><\/td>\n U. B\u00e9jaia<\/strong><\/td>\n Examinateur<\/strong><\/td>\n<\/tr>\n \n Mr Yousfate Abderrahmane<\/strong><\/td>\n Professeur<\/strong><\/td>\n U. Sidi Bel Abess<\/strong><\/td>\n Examinateur<\/strong><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n