Probability and Its Applications: Limit Theory and Statistical Applications

Peña, Victor H.; Lai, Tze Leung; Shao, Qi-Man

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.

Details

Published by: Springer

Publication Date: 2010-11-30

Format: Paperback

ISBN-13: 9783642099267

DOI: 10.1007/978-3-540-85636-8

Dimensions: 235cm x155cm

Pages: 275