| Titre : | On estimation of the hazard function for doubly truncated data |
| Auteurs : | ELBAY Roumaissa, Auteur ; Djabrane Yahia, Auteur |
| Type de document : | Thése doctorat |
| Année de publication : | 2025 |
| Format : | 1 vol. (62 p.) |
| Langues: | Anglais |
| Résumé : |
In this thesis, we investigate the problem of incomplete data, specifically the phenomenon of double truncation, which make working with classical methods very hard, as truncation mean the loss of samples during the statistical analysis, and leads to negative results of the study and wrong decisions. Specifically, we focused in this thesis on estimating of the hazard function in the case of double truncation, where estimating the hazard function estimator is defined in many previous work, hence we make comparison with the hazard functions known in this case and our proposed estimator, and thus we result that the proposed hazard function estimator is more accurate through applied and theoretical comparison. In addition, a smoother cumulative distribution function estimator was proposed, as the previously proposed estimator of the distribution function it was not smooth and not continuous. In this context, several methods were also proposed to obtain the smoothing parameter for the cumulative distribution function within the data subject to double truncation. |
| Sommaire : |
List of Figures List of Tables Symbols and Acronyms General introduction 1 1 Censoring and truncation 4 1.1 Preliminary definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.2 Censoring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.2.1 Types of censoring . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.2.2 A guide to defining likelihood functions with censored data . . . . . . 12 1.2.3 Techniques for estimation in the presence of right censored data . . . 13 1.3 Truncation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 1.3.1 Types of truncation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 1.3.2 The definition of the likelihood functions with truncation data . . . . 18 1.3.3 Techniques for estimation in the presence of right truncated data . . 19 2 Estimation under double truncation 20 2.1 The definition of probability under double truncation . . . . . . . . . . . . . . 21 2.2 The construction of the likelihood function under double truncation data . . . 22 2.2.1 Nonparametric consideration in estimation . . . . . . . . . . . . . . . 22 2.2.2 Semiparametric consideration in estimation . . . . . . . . . . . . . . 26 Contents 2.2.3 Bootstrap method . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 2.2.4 Particular case of double truncation: Fixed-Length . . . . . . . . . . 28 2.3 Kernel density estimator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 2.3.1 Asymptotic properties . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 2.3.2 Selection of optimal bandwidth for kernel density estimator . . . . . . 31 2.4 Kernel estimation of the cumulative distribution function . . . . . . . . . . . 35 2.4.1 Asymptotic properties . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 3 Hazard function for doubly truncated data 38 3.1 The NPMLE of Hazard function . . . . . . . . . . . . . . . . . . . . . . . . . 39 3.2 The smooth estimator of hazard function . . . . . . . . . . . . . . . . . . . . 42 3.3 The proposed estimator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 3.4 Asymptotic properties of the proposed estimator . . . . . . . . . . . . . . . . 46 4 Simulation 48 4.1 Simulation data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 4.2 Analyze the results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 5 On optimal bandwidth selection 56 5.1 Kernel smoothing estimation of the distribution function . . . . . . . . . . . 57 5.1.1 Normal reference bandwidth for the cumulative kernel distribution function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 5.1.2 Plug in method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 5.1.3 Cross-validation method for define the optimal bandwidth . . . . . . . 61 5.1.4 Bootstrap bandwidth selection . . . . . . . . . . . . . . . . . . . . . . 62 Bibliography 3 |
| En ligne : | http://thesis.univ-biskra.dz/id/eprint/6852 |
Disponibilité (1)
| Cote | Support | Localisation | Statut |
|---|---|---|---|
| TM/168 | Théses de doctorat | bibliothèque sciences exactes | Consultable |
