Self-Normalized Processes

I. Independent Random Variables

1. Introduction

2. Classical Limit Theorems, Inequalities and Other Tools

3. Self-Normalized Large Deviations

4. Weak Convergence of Self-Normalized Sums

5. Stein's Method and Self-Normalized Berry–Esseen Inequality

6. Self-Normalized Moderate Deviations and Laws of the Iterated Logarithm

7. Cramér-Type Moderate Deviations for Self-Normalized Sums

8. Self-Normalized Empirical Processes and U-Statistics

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

14. Multivariate Self-Normalized Processes with Matrix Normalization

III. Statistical Applications

15. The t-Statistic and Studentized Statistics

16. Self-Normalization for Approximate Pivots in Bootstrapping

17. Pseudo-Maximization in Likelihood and Bayesian Inference

18. Sequential Analysis and Boundary Crossing Probabilities for Self-Normalized Statistics

Avainsanat: MATHEMATICS / General MAT000000