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Probability for statisticians

Author: Galen R Shorack
Publisher: Cham, Switzerland : Springer, 2017.
Series: Springer texts in statistics
Edition/Format:   eBook : Document : English : Second editionView all editions and formats
Summary:
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  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Printed edition:
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Galen R Shorack
ISBN: 9783319522074 3319522078
OCLC Number: 1005133263
Description: 1 online resource (xxii, 510 pages) : illustrations (some color).
Contents: Preface --
Use of This Text --
Definition of Symbols --
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. Distribution and Quantile Functions --
Chapter 7. Independence and Conditional Distributions --
Chapter 8. WLLN, SLLN, LIL, and Series --
Chapter 9. Characteristic Functions and Determining Classes --
Chapter 10. CLTs via Characteristic Functions --
Chapter 11. Infinitely Divisible and Stable Distributions --
Chapter 12. Brownian Motion and Empirical Processes --
Chapter 13. Martingales --
Chapter 14. Convergence in Law on Metric Spaces --
Chapter 15. Asymptotics Via Empirical Processes --
Appendix A. Special Distributions --
Appendix B. General Topology and Hilbert Space --
Appendix C. More WLLN and CLT --
References --
Index.
Series Title: Springer texts in statistics
Responsibility: Galen R. Shorack.

Abstract:

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  Read more...

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"It discusses measure theoretic probability from the viewpoint of what a theoretical statistician needs to know, and includes many details that an applied statistician may need to look up on Read more...

 
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