| Author |
De la Peña, Víctor.
|
| Series |
Probability and its applications. |
|
Probability and its applications (Springer-Verlag)
|
| Subject |
Probabilities.
|
|
Probability measures.
|
|
Probability.
|
| Alt Name |
Lai, T. L.
|
|
Shao, Qi-Man.
|
| Description |
1 online resource. |
|
polychrome rdacc |
| Bibliography Note |
Includes bibliographical references and index. |
| Note |
Print version record. |
| 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 -- Cramer-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. |
| Summary |
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 period of slow development. In recent years there have been a number of important advances in the theory and applications of self-normalized processes. Some of these developments are closely linked to the study of central limit theorems, which imply that self-normalized processes are approximate pivots for statistical inference. The present volume covers recent developments in the area, including self-normalized large and moderate deviations, and laws of the iterated logarithms for self-normalized martingales. This is the first book that systematically treats the theory and applications of self-normalization. |
| ISBN |
9783540856368 |
|
3540856366 |
|
3540856358 (Cloth) |
|
9783540856351 |
|
3540856358 |
| OCLC # |
314183522 |
| Additional Format |
Print version: De la Pena, Victor. Self-normalized processes. Berlin : Springer, 2009 9783540856351 3540856358 (DLC) 2008938080 (OCoLC)244765605. |
|
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