Fujikoshi / Ulyanov / Shimizu Multivariate Statistics

High-Dimensional and Large-Sample Approximations
1. Auflage 2011
ISBN: 978-0-470-53986-6
Verlag: John Wiley & Sons
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 568 Seiten, E-Book

Reihe: Wiley Series in Probability and Statistics

A comprehensive examination of high-dimensional analysis ofmultivariate methods and their real-world applications
Multivariate Statistics: High-Dimensional and Large-SampleApproximations is the first book of its kind to explore howclassical multivariate methods can be revised and used in place ofconventional statistical tools. Written by prominent researchers inthe field, the book focuses on high-dimensional and large-scaleapproximations and details the many basic multivariate methods usedto achieve high levels of accuracy.
The authors begin with a fundamental presentation of the basictools and exact distributional results of multivariate statistics,and, in addition, the derivations of most distributional resultsare provided. Statistical methods for high-dimensional data, suchas curve data, spectra, images, and DNA microarrays, are discussed.Bootstrap approximations from a methodological point of view,theoretical accuracies in MANOVA tests, and model selectioncriteria are also presented. Subsequent chapters feature additionaltopical 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 indiscriminant analysis, growth curve models, generalized linearmodels, profile analysis, and multiple comparison
Each chapter provides real-world applications and thoroughanalyses of the real data. In addition, approximation formulasfound throughout the book are a useful tool for both practical andtheoretical statisticians, and basic results on exact distributionsin multivariate analysis are included in a comprehensive, yetaccessible, format.
Multivariate Statistics is an excellent book for courseson probability theory in statistics at the graduate level. It isalso an essential reference for both practical and theoreticalstatisticians who are interested in multivariate analysis and whowould benefit from learning the applications of analyticalprobabilistic methods in statistics.

Autoren/Hrsg.

Fujikoshi, Yasunori

Ulyanov, Vladimir V.

Shimizu, Ryoichi

Über Autor(innen)

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