Overview
- First book that systematically treats the theory and applications of Self-Normalization
- Fills a current void in PhD level courses in probability and statistics offered by major Statistics departments
- Rich enough in its coverage to provide such a second course for PhD students
- Integrates advanced probability with theoretical statistics, instead of presenting them as two disparate subjects
- Provides PhD students important tools for their thesis research if they should work on statistical theory
- Includes supplementary material: sn.pub/extras
Part of the book series: Probability and Its Applications (PIA)
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Table of contents (18 chapters)
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Front Matter
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Independent Random Variables
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Martingales and Dependent Random Vectors
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Back Matter
Keywords
About this book
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.
Reviews
From the reviews:
"Readership: Research workers in applied probability. … it serves as a reference text for a special-topic course for PhD students; each chapter after the first ends with a collection of problems and the material is based on such a course taught by two of the authors at Stanford and Hong kong. … It is a thorough … study of an area of applied probability that underlies important statistical methodology. … I am sure that the text will encourage others to join them in their work." (Martin Crowder, International Statistical Review, Vol. 77 (3), 2009)
"The monograph will certainly be of great use as a reference text for researchers working on corresponding problems, but also for Ph.D. and other advanced students who want to learn about the techniques and relevant topics in an interesting and active research area. … this monograph provides a very useful collection of recent and earlier research results in the theory and applications of self-normalized processes and can be used as a standard reference text by graduate students and researchers in the field." (Josef Steinebach, Zentralblatt MATH, Vol. 1165, 2009)
“This book covers recent developments on self-normalized processes, emphasizing important advances in the area. It is the first book that systematically treats the theory and applications of self-normalized processes. … In all aspects, this is an excellent book, and it is ideal for a second-year Ph.D. level topics course. It is also a great book for anyone who is interested in research in self-normalized processes and related areas.” (Fuchang Gao, Mathematical Reviews, Issue 2010 d)Authors and Affiliations
About the authors
Victor H. de la Peña is Fellow of Institute of Mathematical Statistics and a Medallion Lecturer for IMS in 2007.
Tze Leung LAI: Distinguished Lecture Series in Statistical Science from Academia Sinica (2001), Starr Lectures in Financial Mathematics from the University of Hong Kong (2001), Center for Advanced Study in the Behavioral Sciences Fellowship (1999-2000), Richard Anderson Lecture in Statistics from University of Kentucky (1999), Election to Academia Sinica (1994), Committee of Presidents of Statistical Societies Award (1983), John Simon Guggenheim Fellowship (1983-84).
Qi-Man SHAO is Associate Editor of 5 top journals and co-author of: Chen, M. H., Shao, Q. M. and Ibrahim, J.G. (2000) , Monte Carlo Methods In Bayesian Computation . Springer Series in Statistics, Springer-Verlag , New York. ISBN 0-387-98935-8
Bibliographic Information
Book Title: Self-Normalized Processes
Book Subtitle: Limit Theory and Statistical Applications
Authors: Victor H. Peña, Tze Leung Lai, Qi-Man Shao
Series Title: Probability and Its Applications
DOI: https://doi.org/10.1007/978-3-540-85636-8
Publisher: Springer Berlin, Heidelberg
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag Berlin Heidelberg 2009
Hardcover ISBN: 978-3-540-85635-1Published: 28 January 2009
Softcover ISBN: 978-3-642-09926-7Published: 30 November 2010
eBook ISBN: 978-3-540-85636-8Published: 25 December 2008
Series ISSN: 1431-7028
Edition Number: 1
Number of Pages: XIV, 275
Topics: Probability Theory and Stochastic Processes, Statistical Theory and Methods