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.
O autorze
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.
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