Self-Normalized Processes Limit Theory and Statistical Applications /
Self-normalized processes are of common occurrence in probabilistic and statistical studies. A prototypical example is Student's t-statistic introduced in 1908 by Gosset, whose portrait is on the front cover. Due to the highly non-linear nature of these processes, the theory experienced a long...
| Main Authors: | , , |
|---|---|
| Corporate Author: | |
| Format: | Electronic |
| Language: | English |
| Published: |
Berlin, Heidelberg :
Springer Berlin Heidelberg,
2009.
|
| Series: | Probability and its Applications,
|
| Subjects: | |
| Online Access: | https://ezaccess.library.uitm.edu.my/login?url=http://dx.doi.org/10.1007/978-3-540-85636-8 |
Table of Contents:
- 1. Introduction
- Part I Independent Random Variables
- 2. Classical Limit Theorems and Preliminary Tools
- 3. Self-Normalized Large Deviations
- 4. Weak Convergence of Self-Normalized Sums
- 5. Stein<U+0019>s Method and Self-Normalized Berry<U+0013>Esseen Inequality
- 6. Self-Normalized Moderate Deviations and Law of the Iterated Logarithm
- 7. Cramř-type Moderate Deviations for Self-Normalized Sums
- 8. Self-Normalized Empirical Processes and U-Statistics
- Part II Martingales and Dependent Random Vectors
- 9. Martingale Inequalities and Related Tools
- 10. A General Framework for Self-Normalization
- 11. Pseudo-Maximization via Method of Mixtures
- 12. Moment and Exponential Inequalities for Self-Normalized Processes
- 13. Laws of the Iterated Logarithm for Self-Normalized Processes and Martingales
- 14. Multivariate Matrix-Normalized Processes
- Part III Statistical Applications
- 15. The t-Statistic and Studentized Statistics
- 16. Self-Normalization and Approximate Pivots for Bootstrapping
- 17. Self-Normalized Martingales and Pseudo-Maximization in Likelihood or Bayesian Inference
- 18. Information Bounds and Boundary Crossing Probabilities for Self-Normalized Statistics in Sequential Analysis
- References
- Index.