| Titre : | Probability for Statisticians | | Type de document : | texte imprimé | | Auteurs : | Galen R. Shorack, Auteur | | Editeur : | New York : Springer-Verlag | | Année de publication : | 2000 | | Collection : | Springer Texts in Statistics | | Importance : | 585 p. | | Présentation : | couv. ill. en coul., ill. | | Format : | 26 cm. | | ISBN/ISSN/EAN : | 978-0-387-98953-2 | | Langues : | Anglais (eng) | | Mots-clés : | Brownian motion Law of large numbers Martingale mathematical statistics statistics | | Index. décimale : | 25-02 Théorie et traitement du signal | | Résumé : | Probability for Statisticians is intended as a text for a one year graduate course aimed especially at students in statistics. The choice of examples illustrates this intention clearly. The material to be presented in the classroom constitutes a bit more than half the text, and the choices the author makes at the University of Washington in Seattle are spelled out. The rest of the text provides background, offers different routes that could be pursued in the classroom, ad offers additional material that is appropriate for self-study. Of particular interest is a presentation of the major central limit theorems via Stein's method either prior to or alternative to a characteristic funcion presentation. Additionally, there is considerable emphasis placed on the quantile function as well as the distribution function. The bootstrap and trimming are both presented. The martingale coverage includes coverage of censored data martingales. The text includes measure theoretic preliminaries, from which the authors own course typically includes selected coverage. The author is a professor of Statistics and adjunct professor of Mathematics at the University of Washington in Seattle. He served as chair of the Department of Statistics 1986-- 1989. He received his PhD in Statistics from Stanford University. He is a fellow of the Institute of Mathematical Statistics, and is a former associate editor of the Annals of Statistics. | | Note de contenu : | Contents
Chapter 1 Measures
Chapter 2 Measurable Functions and Convergence
Chapter 3 Integration
Chapter 4 Derivatives via Signed Measures
Chapter 5 Measures and Processes on Products
Chapter 6 General Topology and Hilbert Space
Chapter 7 Distribution and Quantile Functions
Chapter 8 Independence and Conditional Distributions
Chapter 9 Special Distributions
Chapter 10 WILL, SLLN, LIL, and Series
Chapter 11 Convergence in Distribution
Chapter 12 Brownian Motion and Empirical Processes
Chapter 13 Characteristic Functions
Chapter 14 CLTs via Characteristic Functions
Chapter 15 Infinitely Divisible and Stable Distributions
Chapter 16 Asymptotics via Empirical Proceses
Chapter 17 Asymptotics via Stein’s Approach
Chapter 18 Martingales
Chapter 19 Convergence in Law on Metric Spaces
Appendix
Index |
Probability for Statisticians [texte imprimé] / Galen R. Shorack, Auteur . - New York : Springer-Verlag, 2000 . - 585 p. : couv. ill. en coul., ill. ; 26 cm.. - ( Springer Texts in Statistics) . ISBN : 978-0-387-98953-2 Langues : Anglais ( eng) | Mots-clés : | Brownian motion Law of large numbers Martingale mathematical statistics statistics | | Index. décimale : | 25-02 Théorie et traitement du signal | | Résumé : | Probability for Statisticians is intended as a text for a one year graduate course aimed especially at students in statistics. The choice of examples illustrates this intention clearly. The material to be presented in the classroom constitutes a bit more than half the text, and the choices the author makes at the University of Washington in Seattle are spelled out. The rest of the text provides background, offers different routes that could be pursued in the classroom, ad offers additional material that is appropriate for self-study. Of particular interest is a presentation of the major central limit theorems via Stein's method either prior to or alternative to a characteristic funcion presentation. Additionally, there is considerable emphasis placed on the quantile function as well as the distribution function. The bootstrap and trimming are both presented. The martingale coverage includes coverage of censored data martingales. The text includes measure theoretic preliminaries, from which the authors own course typically includes selected coverage. The author is a professor of Statistics and adjunct professor of Mathematics at the University of Washington in Seattle. He served as chair of the Department of Statistics 1986-- 1989. He received his PhD in Statistics from Stanford University. He is a fellow of the Institute of Mathematical Statistics, and is a former associate editor of the Annals of Statistics. | | Note de contenu : | Contents
Chapter 1 Measures
Chapter 2 Measurable Functions and Convergence
Chapter 3 Integration
Chapter 4 Derivatives via Signed Measures
Chapter 5 Measures and Processes on Products
Chapter 6 General Topology and Hilbert Space
Chapter 7 Distribution and Quantile Functions
Chapter 8 Independence and Conditional Distributions
Chapter 9 Special Distributions
Chapter 10 WILL, SLLN, LIL, and Series
Chapter 11 Convergence in Distribution
Chapter 12 Brownian Motion and Empirical Processes
Chapter 13 Characteristic Functions
Chapter 14 CLTs via Characteristic Functions
Chapter 15 Infinitely Divisible and Stable Distributions
Chapter 16 Asymptotics via Empirical Proceses
Chapter 17 Asymptotics via Stein’s Approach
Chapter 18 Martingales
Chapter 19 Convergence in Law on Metric Spaces
Appendix
Index |
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Probability for Statisticians / Galen R. Shorack
