Probability for Statisticians de Galen R. Shorack

Probability for Statisticians: Springer Texts in Statistics

en Limba Engleză Paperback – 15 mar 2013

The choice of examples used in this text clearly illustrate its use for a one-year graduate course. The material to be presented in the classroom constitutes a little more than half the text, while the rest of the text provides background, offers different routes that could be pursued in the classroom, as well as additional material that is appropriate for self-study. Of particular interest is a presentation of the major central limit theorems via Steins method either prior to or alternative to a characteristic function presentation. Additionally, there is considerable emphasis placed on the quantile function as well as the distribution function, with both the bootstrap and trimming presented. The section on martingales covers censored data martingales.

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Specificații

ISBN-13: 9781475774009
ISBN-10: 1475774001
Pagini: 608
Dimensiuni: 178 x 254 x 32 mm
Greutate: 1.04 kg
Ediția:Softcover reprint of the original 1st ed. 2000
Editura: Springer
Colecția Springer
Seria Springer Texts in Statistics

Locul publicării:New York, NY, United States

Public țintă

Graduate

Descriere

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.

Cuprins

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.

Recenzii

From the reviews:
"This book offers a rigorous introduction to measure theoretic probability with particular attention to topics of interest to mathematical statisticians. ... recommended to anyone interseted in the probability underlying modern statistics."
D.L. McLeish in "Short Book Reviews", Vol. 21/1, April 2001

"The book originated from a graduate level course given by the author on probability at the University of Washington, Seattle. It is an excellent textbook for a course in probability for students in mathematical statistics. It provides a solid grounding in the probabilistic tools and techniques that are necessary to do theoretical research in statistics.
For the teaching of probability theory to post graduate statistics students, this is certainly one of the most attractive books available and is highly recommended for that purpose. It is also an extremely good reference source of value to any research statistician.
SASA News, Dec. 2001
"This book contains a wealth of material and is very rigorous. It may serve as a good reference book and as a source for a graduate course in probability. … The author provides detailed notes on the use of the text for a graduate course of probability. … Overall, this is an excellent book to acquire." (Arup Bose, Sankhya, Vol. 64 (1), 2002)
"The present textbook grew out of probability lecturers given at the University of Washington in Seattle. … is an excellent reference. The present monograph can strongly be recommended. It is a highlight in modern probability theory with strong applications to mathematical statistics. It may serve as a textbook for advanced lecturers and seminars but it is also worthwhile as reference book for modern aspects in probability theory. … I am happy to have this book on my desk." (Arnold Janssen, Metrika, April, 2001)
"This is a textbook about probability theory, with a view towards applications in statistics. … The book contains 585 pages of text. It contains a lot of useful material which every theoretical statistician should know. … All in all, this is an interesting book and certainly recommended." (R. Helmers, Kwantitatieve Methoden, Vol. 22 (68), 2001)
"This text covers a broad range of probability theory with special emphasis on fields which are useful for statistics. One characteristic unique to this text is the presentation of different approaches to the CLT. The presentation is in the style: definition – proposition/theorem – proof. More detailed motivations are concentrated in special paragraphs. Questions are included to open the view for further generalizations and motivate the reader to think themselves. Exercises are everywhere." (R. Schlittgen, Zentralblatt MATH, Vol. 951, 2001)

Notă biografică

Galen Shorack, PhD, is Professor Emeritus in the Department of Statistics (of which he was a founding member) and Adjunct Professor in the Department of Mathematics at the University of Washington, Seattle. He received his Bachelor of Science and Master of Science degrees in Mathematics from the University of Oregon and his PhD in Statistics from Stanford University. Dr. Shorack's research interests include limit theorems in statistics, the theory of empirical processes, trimming-Winsorizing, and regular variation. He has served as Associate Editor of the Annals of Mathematical Statistics (Annals of Statistics) and is Fellow of the Institute of Mathematical Statistics.

Textul de pe ultima copertă

This 2nd edition textbook offers a rigorous introduction to measure theoretic probability with particular attention to topics of interest to mathematical statisticians—a textbook for courses in probability for students in mathematical statistics. It is recommended to anyone interested in the probability underlying modern statistics, providing a solid grounding in the probabilistic tools and techniques necessary to do theoretical research in statistics. For the teaching of probability theory to post graduate statistics students, this is one of the most attractive books available.
Of particular interest is a presentation of the major central limit theorems via Stein's method either prior to or alternative to a characteristic function presentation. Additionally, there is considerable emphasis placed on the quantile function as well as the distribution function. The bootstrap and trimming are both presented. Martingale coverage includes coverage of censored data martingales. The text includes measure theoretic preliminaries, from which the authors own course typically includes selected coverage.

This is a heavily reworked and considerably shortened version of the first edition of this textbook. "Extra" and background material has been either removed or moved to the appendices and important rearrangement of chapters has taken place to facilitate this book's intended use as a textbook.

New to this edition:

Still up front and central in the book, Chapters 1-5 provide the "measure theory" necessary for the rest of the textbook and Chapters 6-7 adapt that measure-theoretic background to the special needs of probability theory
Develops both mathematical tools and specialized probabilistic tools
Chapters organized by number of lectures to cover requisite topics, optional lectures, and self-study
Exercises interspersed within the text
Guidance provided to instructors to help in choosing topics of emphasis

Caracteristici

Still up front and central in the book, Chapters 1-5 provide the "measure theory" necessary for the rest of the textbook and Chapters 6-7 adapt that measure-theoretic background to the special needs of probability theory Develops both mathematical tools and specialized probabilistic tools Chapters organized by number of lectures to cover requisite topics, optional lectures, and self-study Exercises interspersed within the text Guidance provided to instructors to help in choosing topics of emphasis Includes supplementary material: sn.pub/extras

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