Multivariate Statistics (eBook)

High-Dimensional and Large-Sample Approximations

Yasunori Fujikoshi, Vladimir V. Ulyanov, Ryoichi Shimizu (Autoren)

eBook Download: PDF

2011 | 1. Auflage
568 Seiten
John Wiley & Sons (Verlag)
978-0-470-53986-6 (ISBN)

Infos

A comprehensive examination of high-dimensional analysis of
multivariate methods and their real-world applications

Multivariate Statistics: High-Dimensional and Large-Sample
Approximations is the first book of its kind to explore how
classical multivariate methods can be revised and used in place of
conventional statistical tools. Written by prominent researchers in
the field, the book focuses on high-dimensional and large-scale
approximations and details the many basic multivariate methods used
to achieve high levels of accuracy.

The authors begin with a fundamental presentation of the basic
tools and exact distributional results of multivariate statistics,
and, in addition, the derivations of most distributional results
are provided. Statistical methods for high-dimensional data, such
as curve data, spectra, images, and DNA microarrays, are discussed.
Bootstrap approximations from a methodological point of view,
theoretical accuracies in MANOVA tests, and model selection
criteria are also presented. Subsequent chapters feature additional
topical coverage including:

* High-dimensional approximations of various statistics

* High-dimensional statistical methods

* Approximations with computable error bound

* Selection of variables based on model selection approach

* Statistics with error bounds and their appearance in
discriminant analysis, growth curve models, generalized linear
models, profile analysis, and multiple comparison

Each chapter provides real-world applications and thorough
analyses of the real data. In addition, approximation formulas
found throughout the book are a useful tool for both practical and
theoretical statisticians, and basic results on exact distributions
in multivariate analysis are included in a comprehensive, yet
accessible, format.

Multivariate Statistics is an excellent book for courses
on probability theory in statistics at the graduate level. It is
also an essential reference for both practical and theoretical
statisticians who are interested in multivariate analysis and who
would benefit from learning the applications of analytical
probabilistic methods in statistics.

Autor

Yasunori Fujikoshi, DSc, is Professor Emeritus at Hiroshima University (Japan) and Visiting Professor in the Department of Mathematics at Chuo University (Japan). He has authored over 150 journal articles in the area of multivariate analysis. Vladimir V. Ulyanov, DSc, is Professor in the Department of Mathematical Statistics at Moscow State University (Russia) and is the author of nearly fifty journal articles in his areas of research interest, which include weak limit theorems, probability measures on topological spaces, and Gaussian processes. Ryoichi Shimizu, DSc, is Professor Emeritus at the Institute of Statistical Mathematics (Japan) and is the author of numerous journal articles on probability distributions.

Rezensionen

"The book is designed for readers interested in multivariate
analysis with a good background in matrix algebra, mathematical
statistical inference and probability theory. Its contents are, in
general, well organised and the intuitive ideas behind the
different multivariate methods, the asymptotic expansion techniques
and the calculation of error bounds using scale mixtures, are well
expressed . The mathematical proofs are well presented and selected
and I have found the mathematical appendices to be very useful as
guides to following the proofs." (Mathematical Reviews, 2011)

Produkt-Details

• Erscheint lt. Verlag: 15.8.2011
• Reihe/Serie: Wiley Series in Probability and Statistics
• Reihe/Serie: Wiley Series in Probability and Statistics
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Statistik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
• Themenwelt: Technik
• Schlagworte: Methoden der Daten- u. Stichprobenerhebung • Multivariate Analyse • multivariate analysis • Statistics • Statistik • Stichprobe • Survey Research Methods & Sampling
• ISBN-10: 0-470-53986-0 / 0470539860
• ISBN-13: 978-0-470-53986-6 / 9780470539866