Self-Normalized Processes : Limit Theory and Statistical Applications
Overview
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.
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Details
- ISBN-13: 9783642099267
- ISBN-10: 3642099262
- Publisher: Springer
- Publish Date: November 2010
- Dimensions: 9.21 x 6.14 x 0.61 inches
- Shipping Weight: 0.91 pounds
- Page Count: 275
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