Probability for Statisticians / by Galen R. Shorack.

Format:

Book

Author/Creator:

Shorack, Galen R., Author.

Series:

Springer Texts in Statistics, 2197-4136

Language:

English

Subjects (All):

Statistics.

Probabilities.

Measure theory.

Statistical Theory and Methods.

Probability Theory.

Measure and Integration.

Local Subjects:

Statistical Theory and Methods.

Probability Theory.

Measure and Integration.

Physical Description:

1 online resource (XXII, 510 p. 19 illus., 15 illus. in color.)

Edition:

2nd ed. 2017.

Place of Publication:

Cham : Springer International Publishing : Imprint: Springer, 2017.

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 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.

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.

ISBN:

3-319-52207-8

OCLC:

1005133263