Probability for Statisticians

• Main Author: Shorack, Galen R. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2017.
• Edition: 2nd ed. 2017.
• Series: Springer Texts in Statistics,
• Subjects: Statistics.; Measure theory.; Probabilities.; Statistical Theory and Methods.; Probability Theory and Stochastic Processes.; Measure and Integration.

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 probabi...

Table of 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.