Self-Normalized Processes: Limit Theory and Statistical Applications

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’s Method and Self-Normalized Berry–Esseen Inequality.- 6. Self-Normalized Moderate Deviations and Law of the Iterated Logarithm.- 7. Cramér-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.