Self-Normalized Processes: Limit Theory and Statistical Applications

By Tze Leung Lai, Qi-Man Shao, Victor H. Peña

Independent Random Variables.- Classical Limit Theorems, Inequalities and Other Tools.- Self-Normalized Large Deviations.- Weak Convergence of Self-Normalized Sums.- Stein's Method and Self-Normalized Berry-Esseen Inequality.- Self-Normalized Moderate Deviations and Laws of the Iterated Logarithm.- Cram r-Type Moderate Deviations for Self-Normalized Sums.- Self-Normalized Empirical Processes and U-Statistics.- Martingales and Dependent Random Vectors.- Martingale Inequalities and Related Tools.- A General Framework for Self-Normalization.- Pseudo-Maximization via Method of Mixtures.- Moment and Exponential Inequalities for Self-Normalized Processes.- Laws of the Iterated Logarithm for Self-Normalized Processes.- Multivariate Self-Normalized Processes with Matrix Normalization.- Statistical Applications.- The t-Statistic and Studentized Statistics.- Self-Normalization for Approximate Pivots in Bootstrapping.- Pseudo-Maximization in Likelihood and Bayesian Inference.- Sequential Analysis and Boundary Crossing Probabilities for Self-Normalized Statistics.

• Format: Paperback
• Language: English
• ISBN: 3642099262
• ISBN13: 9783642099267
• Release Date: November 2010
• Publisher: Springer
• Length: 275 Pages
• Weight: 0.91 lbs.
• Dimensions: 0.6" x 6.1" x 9.2"