Probability for Statisticians
Springer International Publishing (Verlag)
978-3-319-52206-7 (ISBN)
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.
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.
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.
"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 occasion. Reading it frequently feels like you are sitting next to the author, with him pointing out the important parts, and suggesting how to think about things. I enjoyed that aspect very much, and it helps to solidify the readers understanding." (Peter Rabinovitch, MAA Reviews, January, 2018)
| Erscheinungsdatum | 14.10.2017 |
|---|---|
| Reihe/Serie | Springer Texts in Statistics |
| Zusatzinfo | XXII, 510 p. 19 illus., 15 illus. in color. |
| Verlagsort | Cham |
| Sprache | englisch |
| Maße | 178 x 254 mm |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik | |
| Schlagworte | Brownian motion • central limit theorem • Distribution • Integral calculus and equations • law of large numbers • Martingale • mathematics and statistics • measure and integration • measure theory • probability and statistics • Probability Theory • Probability theory and stochastic processes • Statistical Theory and Methods • stochastics |
| ISBN-10 | 3-319-52206-X / 331952206X |
| ISBN-13 | 978-3-319-52206-7 / 9783319522067 |
| Zustand | Neuware |
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