| Titre : | On robust tail index extimation under incomplete data |
| Auteurs : | Abida ZAHNIT, Auteur ; Brahim Brahimi, 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, 2022 |
| Format : | 1 vol. (70 p.) / couv. ill. en coul / 30 cm |
| Langues: | Français |
| Résumé : |
In this thesis, we propose a new robust estimation procedure for the tail index for Pareto-type distributions under incomplete data (censorship or truncation). Under truncation, the extreme quantile estimation is also derived and applied to an actual data set on automobile brake pad life. Simulation study using R statistical software is carried out to evaluate the performance and the robustness of the proposed estimators for small and large sample size and for both uncontaminated and contaminated cases. Our newly estimators have been shown to be more robust and perform better than existing Hill-type estimators based on upper order statistics, in both cases of incomplete data (censorshipor truncation) |
| Sommaire : |
Contents Dedicace i Acknowledgments ii Achieved Works iii Abstract iv Notations and symbols v Contents vii Liste of Ögures x Liste of tables xi RÈsumÈ de la thËse 1 Introduction 4 1 Heavy-tailed distributions and extreme value theory 9 1.1 Heavy-tailed distributions . . . . . . . . . . . . . . . . . . . . . . 9 vii 1.1.1 Examples of heavy-tailed distributions . . . . . . . . . . . 13 1.1.2 Regularly varying distribution functions . . . . . . . . . . 15 1.2 Extreme value theory . . . . . . . . . . . . . . . . . . . . . . . . . 16 1.2.1 Extreme value distributions . . . . . . . . . . . . . . . . . 16 1.2.2 Tail index estimation . . . . . . . . . . . . . . . . . . . . . 20 1.2.3 Robust estimation vs upper quantile . . . . . . . . . . . . 22 2 Incomplete data context 25 2.1 Censoring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 2.1.1 Censoring Types . . . . . . . . . . . . . . . . . . . . . . . 26 2.1.2 Framework of randomly right censoring . . . . . . . . . . . 27 2.2 Truncation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 2.2.1 Truncation Types . . . . . . . . . . . . . . . . . . . . . . . 29 2.2.2 Estimation under right truncation . . . . . . . . . . . . . . 31 3 Robust tail index estimation under censoring 33 3.1 Hill-type estimator under censoring . . . . . . . . . . . . . . . . . 34 3.2 Robust tail index estimation and asymptotic results . . . . . . . . 36 3.3 Performance and comparative study . . . . . . . . . . . . . . . . . 42 3.4 Comparative robustness study . . . . . . . . . . . . . . . . . . . . 43 4 Robust tail index estimation under truncation 46 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 4.2 Framework and statement of the results . . . . . . . . . . . . . . . 51 4.3 Simulation study . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 4.4 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 4.4.1 Estimation of an upper quantile . . . . . . . . . . . . . . . 56 4.4.2 Real data example : automobile brake pad lifetime . . . . 57 4.5 Proofs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 Conclusion and Perspectives 64 Bibliography |
| En ligne : | http://thesis.univ-biskra.dz/5690/1/Th%C3%A8se%20ZAHNIT%20A%2022-03-22.pdf |
Disponibilité (1)
| Cote | Support | Localisation | Statut |
|---|---|---|---|
| TM/122 | Théses de doctorat | bibliothèque sciences exactes | Consultable |
