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Self-Normalized Processes: Limit Theory and Statistical Applications

Self-Normalized Processes: Limit Theory and Statistical Applications

Paperback

Series: Probability and Its Applications

Probability & Statistics

ISBN10: 3642099262
ISBN13: 9783642099267
Publisher: Springer
Published: Nov 30 2010
Pages: 275
Weight: 0.91
Height: 0.61 Width: 6.14 Depth: 9.21
Language: English
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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