Limit Theory and Statistical Applications
Series: Probability and Its Applications
Peña, Victor H., Lai, Tze Leung, Shao, Qi-Man
2009, XIV, 275 p.
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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.
Content Level » Research
Keywords » Bootstrapping - Likelihood - Random variable - bootstrap - calculus - large and moderate deviations - law of the iterated logarithm - self-normalization - sequential analysis - studentized U-statistic - t-statistic
Related subjects » Probability Theory and Stochastic Processes - Statistical Theory and Methods
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