| Titre : | Equations différentielles stochastique rétrogrades de type champ moyen |
| Auteurs : | Nassima CHAOUCHKHOUANE, Auteur ; Djabrane Yahia, Directeur de thèse |
| Type de document : | Monographie imprimée |
| Editeur : | Biskra [Algérie] : Faculté des Sciences Exactes et des Sciences de la Nature et de la Vie, Université Mohamed Khider, 2016 |
| Format : | 1 vol. (107 p.) / couv. ill. / 30 cm |
| Langues: | Français |
| Résumé : |
In this thesis we study some boundary correction methods for kernel estimators of both density and regression functions and their statistical properties. Kernel estimators are not consistent near the Önite end points of their supports. In other words, these e§ects seriously a§ect the performance of these estimators. To remove the boundary e§ects, a variety of methods have been developed in the literature, the most widely used is the reáection, the transformation and the local linear methods... In this thesis, we combine the transformation and the reáection methods in order to introduce a new general method of boundary correction when estimating the regression function. Boundary problem for kernel quantile function estimator in heavy-tailed case are also studied in this thesis. |
| Sommaire : |
DÈdicace i Remerciements ii Abstract (In Arab) iii Abstract iv RÈsumÈ v Table of Contents vi List of Figures x List of Tables xi Introduction 1 1 Boundary correction in kernel density estimation 5 1.1 Kernel density estimation . . . . . . . . . . . . . . . . . . . . . . 6 1.2 Boundary e§ects . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.3 Boundary corrections in kernel density estimation . . . . . . . . . 13 1.3.1 Cut-and-Normalized method . . . . . . . . . . . . . . . . . 15 1.3.2 Reáection of the data method . . . . . . . . . . . . . . . . 15 1.3.3 Generalized JackkniÖng method . . . . . . . . . . . . . . . 18 1.3.4 Translation in the argument of the kernel method . . . . . 21 1.3.5 Reáection and transformation methods . . . . . . . . . . . 23 1.3.6 Riceís boundary modiÖcation density estimator . . . . . . 26 2 Boundary correction in kernel regression estimation 29 2.1 Nadaraya-Watson estimator . . . . . . . . . . . . . . . . . . . . . 30 2.2 Some boundary corrections methods in kernel regression estimation 31 2.2.1 Gasser and M¸ller estimator . . . . . . . . . . . . . . . . . 33 2.2.2 Cut-and-Normalized regression estimator . . . . . . . . . . 34 2.2.3 Riceís boundary modiÖed regression estimator . . . . . . . 36 2.2.4 Generalized Jackknif regression estimator . . . . . . . . . . 37 2.2.5 Local linear regression estimator . . . . . . . . . . . . . . . 40 3 General method of boundary correction in kernel regression estimation 44 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 3.2 Main results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 3.3 Simulation results . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 3.4 Proofs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 4 Boundary correction using the Champernowne transformation 63 4.1 Champernowne transformation . . . . . . . . . . . . . . . . . . . 64 4.2 Boundary correction for heavy-tailed distributions . . . . . . . . . 66 4.3 Boundary correction in kernel quantile estimation . . . . . . . . . 68 4.3.1 Kernel quantile estimation . . . . . . . . . . . . . . . . . . 68 4.3.2 Estimation procedure . . . . . . . . . . . . . . . . . . . . . 71 4.3.3 Asymptotic theory and bandwidth selection . . . . . . . . 72 4.4 Examples and comparative study . . . . . . . . . . . . . . . . . . 74 Conclusion 77 Bibliography 80 Symbols and Notations 90 |
| En ligne : | http://thesis.univ-biskra.dz/2600/1/Th%C3%A8se_47_2016.pdf |
Disponibilité (1)
| Cote | Support | Localisation | Statut |
|---|---|---|---|
| TM/57 | Théses de doctorat | bibliothèque sciences exactes | Consultable |
