Probability for Statisticians

• Κύριος συγγραφέας: Shorack, Galen R. (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: New York, NY : Springer New York, 2000.
• Σειρά: Springer Texts in Statistics,
• Θέματα: Mathematics.; Probabilities.; Statistics.; Probability Theory and Stochastic Processes.; Statistics, general.

 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. 

 Measures -- Measurable Functions and Convergence -- Integration -- Derivatives via Signed Measures -- Measures and Processes on Products -- General Topology and Hilbert Space -- Distribution and Quantile Functions -- Independence and Conditional Distributions -- Special Distributions -- WLLN, SLLN, LIL, and Series -- Convergence in Distribution -- Brownian Motion and Empirical Processes -- Characteristic Functions -- CLTs via Characteristic Functions -- Infinitely Divisible and Stable Distributions -- Asymptotics via Empirical Proceses -- Asymptotics via Stein’s Approach -- Martingales -- Convergence in Law on Metric Spaces.