| Titre : | On the Estimation of the Distribution Tail Index |
| Auteurs : | Zahia Khemessi, Auteur ; Brahim Brahimi, Directeur de thèse ; 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, 2023 |
| Format : | 1 vol. (78 p.) / couv. ill. en coul / 30 cm |
| Langues: | Anglais |
| Mots-clés: | Extreme value Theory, Extreme value index, Heavy-tails, Least squares estimator, Weighted least squares, Rank regression, Frechet distribution. |
| Résumé : |
This thesis is devoted to the study of a regression estimator for estimating the tail index of the heavy-tailed distribution. In particular, it is shown that the considered estimator is in general based on the method of weighted least squares. The main objective of the thesis is extend the work of Zyl and schall; 2012, for estimating the shape parameter of the Frechet distribution. By deriving the large sample variances and using the inverse of the approximate variance to calculate the weights for this estimator. Simulation study using R statistical software is carried out to evaluate performance of a new estimator wich has been shown to perform better than other considered methods estimator based on order statistics for small and large sample size, and in case of real data. |
| Sommaire : |
Contents Dedication i Acknowledgments ii Sienti…c contributions iii Abstract iv Abreviations and notations v Contents vi List of Figures x List of Tables xi Introduction 1 I Preliminary Theory 4 1 Extreme value theory 5 1.1 Foundations de…nition . . . .. . . . . . 5 1.1.1 Order statistics . . . . . .. . . . . . . 7 1.2 Distribution of extreme values . . . .. . . . 8 vii1.2.1 Limit distributions . . .. . . . 9 1.3 Domain of attraction . . . . . . . . . . 13 1.3.1 Characterizations of domain attraction . . .. . . 14 1.4 Tail Index Estimators . . . . . . . . . . . . . . 17 1.4.1 Semi-parametric estimators . . . . . 17 1.4.2 Parametric estimators . . . . . . 22 2 Regression conceptions 27 2.1 The simple regression model . . . . . . . . . 28 2.1.1 De…nitions . . . . . . . . . . . . . . . 28 2.2 Parameter estimation methods . . . . .. . . 31 2.2.1 The least squares method . . . . 31 2.2.2 The weighted least squares method . . . 36 3 A weighted least-squares estimation method for distributional parameters 45 3.1 Preliminary . . . . .. . 45 3.2 Estimation of distributional parameters by regression models . .. . 46 3.3 Expressions of the weights . . . . . . . . . 49 3.3.1 Expressions using a weights functions . . . . . . 49 3.3.2 Expressions using derivation of weights for least-squares . . . . . . . 51 3.4 Simulation results . . . . . . 54 II Main results 58 4 Heavy tail index estimator through weighted least-squares rank regression 59 4.1 Introduction . . . 59 4.2 Estimators and main results . . . 61 4.2.1 Least squares method . . . . . . 61 4.2.2 Weighted Least Squares method . . . . . . 63 4.3 Simulation study and application . . .. . . . . 65 4.3.1 Performance of the estimator . . . . . 65 4.3.2 Results and discussion . . . . . 65 4.3.3 Real data example .. 66 Conclusion 71 Bibliographie 72 |
| En ligne : | http://thesis.univ-biskra.dz/id/eprint/6038 |
Disponibilité (1)
| Cote | Support | Localisation | Statut |
|---|---|---|---|
| TM/138 | Théses de doctorat | bibliothèque sciences exactes | Consultable |
