Self-Normalized Processes: Limit Theory and Statistical Applications

Self-Normalized Processes: Limit Theory and Statistical Applications

English | ISBN: 3540856358 | 2009 | 275 Pages | PDF | 4 MB

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.


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