Self-Normalized Processes Limit Theory and Statistical Applications /

• Main Authors: Peña, Victor H. de la (Author), Lai, Tze Leung (Author), Shao, Qi-Man (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg, 2009.
• Series: Probability and its Applications,
• Subjects: Mathematics.; Probabilities.; Statistics.; Probability Theory and Stochastic Processes.; Statistical Theory and Methods.

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...

Table of Contents:

• 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
• Cramér-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.