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...

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Bibliographic Details
Call Number:Libro Electrónico
Main Authors: Peña, Victor H. (Author), Lai, Tze Leung (Author), Shao, Qi-Man (Author)
Corporate Author: SpringerLink (Online service)
Format: Electronic eBook
Language:Inglés
Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2009.
Edition:1st ed. 2009.
Series:Probability and Its Applications
Subjects:
Probabilities.
Statistics .
Probability Theory.
Statistical Theory and Methods.
Online Access:Texto Completo
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.

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