| Titre : | Nonparametric Estimation of the Copula Function with Bivariate Twice Censored Data |
| Auteurs : | Samia Toumi, Auteur ; Fatah Benatia, Directeur de thèse |
| Type de document : | Thése doctorat |
| Editeur : | Biskra [Algérie] : Faculté des Sciences Exactes et des Sciences de la Nature et de la Vie, Université Mohamed Khider, 2024 |
| Format : | 1 vol. (70 p.) / ill., couv. ill. en coul / 30 cm |
| Langues: | Anglais |
| Mots-clés: | Copulas, empirical copula process, twice censored data, product-limit estimator, Smoothed estimators, weak convergence. |
| Résumé : |
The aim of this thesis is to study the nonparametric estimation of the copula funct ion in the presence of bivariate twice censored data. Assuming that the copula functions of the right and the left censoring variables are known, we propose an estimator of the joint distribution function of the variables of interest, then we derive an estimator of their copula function. Using a representation of the proposed estimator of the joint distribution function as a sum of independent and identically distributed variables, we establish the weak convergence of the empirical copula and simulation. After that, we studied the kernel estimation of the copula function of two twice censored random variables. So, we introduce two kernel estimators of the joint distribution function of the two variables of interest. Then, we use these estimators to propose two smoothed estimators of the copula function. We also prove the weak convergence of the proposed estimators to some tight centered Gaussian processes. Finally, we illustrate the performances of our estimators through a simulation study.
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| Sommaire : |
Résumé ii
Abstract iii Introduction 11 1 Preliminaries 16 2 Copula Conseption 19 2.1 Bivariate Copula . . . . . . . . . . 19 2.1.1 Density of the copula . . . . . . . . . . . . .. . . . . 20 2.1.2 Copula properties . . . . . . . . . . . . . . . . . . 20 2.2 Bivariate copula families . . . . . . . . . . . . . . . . . . 21 2.2.1 Usual Copulas . . . . . . . . . . . . . . . . . . . 22 2.2.2 Elliptique copula . . . . . . . . . . . . . . . 22 2.2.3 Gaussian copula . . . . . . . . . . 22 2.2.4 Student copula . . . . . . . . . . . . 23 2.2.5 Emprical Copula . . . . . . . . 28 3.0.2 Non-parametric estimation for right-censoring model . 29 3.0.3 Non-parametric estimation for mixed censoring model . . 31 3.0.4 Smooth estimators of the copula and its density . . . 32 3.0.5 Semi-parametric estimation for Copula models . . . . . . . . . .. 33 4 Simulation of the Copula Function with Bivariate Twice Censored Data 35 4.1 Empirical copula for twice censored data . . . . 35 4.2 Main results . . . . . . . . . . . . . . . . . . . . . . .. . . . 37 4.3 Simulation study . . . . . . . . . . . . . . . . 42 5 Kernel estimation of the copula function under twice censoring 45 5.1 Kernel copula estimators . . . . . . . . . . . . . . . . . . . . 45 5.2 Weak convergence of the proposed estimators . . . . . . . . 47 5.3 Simulation study . . . . . . . . . . . . . . . . . . . .. . . 49 Conclusion 54 Appendix 55 5.4 Proofs . . . . . . . . . . 55 Bibliography 70 |
| En ligne : | http://thesis.univ-biskra.dz/id/eprint/6555 |
Disponibilité (1)
| Cote | Support | Localisation | Statut |
|---|---|---|---|
| TM/155 | Théses de doctorat | bibliothèque sciences exactes | Consultable |
