| Titre : | Conditional quantile for truncated dependent data |
| Auteurs : | YAHIA Djabrane, Auteur ; Abdelhakim Necir , 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, 2010 |
| Format : | 1 vol. (94 p.) / couv. ill. / 30 cm |
| Langues: | Anglais |
| Mots-clés: | Asymptotic normality ; Conditional quantile ; Kernel estimate ; Strong mixing ; Strong uniform consistency ; Truncated data. |
| Résumé : | In this thesis we study some asymptotic properties of the kernel conditional quantile estimator when the interest variable is subject to randomleft truncation. The uniform strong convergence rate of the estimator is obtained. In addition, it is shown that, under regularity conditions and suitably normalized, the kernel estimate of the conditional quantile is asymptotically normally distributed. Our interest in conditional quantile estimation is motivated by it�s robusteness, the constructing of the con�dence bands and the forecasting from time series data. Our results are obtained in a more general setting (strong mixing) which includes time series modelling as a special case. |
| Sommaire : |
Remerciements ii
Cotutelle iii Accord des Commissions des ThËses iv Abstract v RÈsumÈ vi Achieved Works vii Avant-propos viii Introduction 1 1 Basic concepts 4 1.1 Incomplete data . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.1.1 Censoring . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.1.2 Truncation . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.2 Mixing conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.2.1 DeÖnitions and properties . . . . . . . . . . . . . . . . . . 7 1.2.2 Strong mixing conditions . . . . . . . . . . . . . . . . . . . 8 2 Estimation under random left-truncation model 10 2.1 Random left-truncation model . . . . . . . . . . . . . . . . . . . . 10 2.2 Estimation of the truncation probability . . . . . . . . . . . . . . 12 2.3 Estimation of the covariateís density . . . . . . . . . . . . . . . . 17 3 A strong uniform convergence rate... 19 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 3.2 DeÖnition of the estimator . . . . . . . . . . . . . . . . . . . . . . 22 3.3 Assumptions and main results . . . . . . . . . . . . . . . . . . . . 25 3.4 Applications to prediction . . . . . . . . . . . . . . . . . . . . . . 27 xii CONTENTS xiii 3.5 Proofs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 4 Asymptotic normality... 40 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 4.2 The model, the assumptions and the main results . . . . . . . . . 43 4.3 Application to prediction . . . . . . . . . . . . . . . . . . . . . . . 49 4.4 Proofs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 Conclusion 68 Appendix A. CramÈr-Wold device 69 Appendix B. Stochastic o and O symbols 70 Appendix C. Notations and abbreviations 71 Bibliography 72 |
| En ligne : | http://thesis.univ-biskra.dz/1788/1/Math-d-2010.pdf |
Disponibilité (1)
| Cote | Support | Localisation | Statut |
|---|---|---|---|
| TM/38 | Théses de doctorat | bibliothèque sciences exactes | Consultable |
