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Self-Normalized Processes

Limit Theory and Statistical Applications

Self-Normalized Processes by Victor H. Peña
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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.

Springer Berlin Heidelberg; December 2008
283 pages; ISBN 9783540856368
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Title: Self-Normalized Processes
Author: Victor H. Peña; Tze Leung Lai; Qi-Man Shao
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