Self-Normalized Processes (eBook)

Victor H. de la Peña is Fellow of Institute of Mathematical Statistics and a Medallion Lecturer for IMS in 2007. Tze Leung LAI: Distinguished Lecture Series in Statistical Science from Academia Sinica (2001), Starr Lectures in Financial Mathematics from the University of Hong Kong (2001), Center for Advanced Study in the Behavioral Sciences Fellowship (1999-2000), Richard Anderson Lecture in Statistics from University of Kentucky (1999), Election to Academia Sinica (1994), Committee of Presidents of Statistical Societies Award (1983), John Simon Guggenheim Fellowship (1983-84). Qi-Man SHAO is Associate Editor of 5 top journals and co-author of: Chen, M. H., Shao, Q. M. and Ibrahim, J.G. (2000) , Monte Carlo Methods In Bayesian Computation . Springer Series in Statistics, Springer-Verlag , New York. ISBN 0-387-98935-8

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.