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Self-Normalized Processes : Limit Theory and Statistical Applications / by Victor H. Peña, Tze Leung Lai, Qi-Man Shao; edited by Joe Gani, C. C. Heyde, P. Jagers, T. G. Kurtz

Contributor(s): Resource type: Ressourcentyp: Buch (Online)Book (Online)Language: English Series: Probability and its Applications | SpringerLink BücherPublisher: Berlin, Heidelberg : Springer Berlin Heidelberg, 2009Description: Online-Ressource (digital)ISBN:
  • 9783540856368
Subject(s): Additional physical formats: 9783540856351 | Buchausg. u.d.T.: Self-normalized processes. Berlin : Springer, 2009. XI, 250 S. | Erscheint auch als: Self-normalized processes. Druck-Ausgabe Berlin [u.a.] : Springer, 2009. XIII, 275 S.DDC classification:
  • 519.24
  • 519.2
MSC: MSC: *62M99 | 62-02 | 60Gxx | 60-02 | 60Fxx | 62L99 | 62Gxx | 62JxxRVK: RVK: SK 800 | SK 820LOC classification:
  • QA273.A1-274.9 QA274-274.9
  • QA273
DOI: DOI: 10.1007/978-3-540-85636-8Online resources: Summary: 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.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.PPN: PPN: 1647673216Package identifier: Produktsigel: ZDB-2-SEB | ZDB-2-SXMS | ZDB-2-SMA
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