Multivariate Statistics - Fujikoshi, Yasunori; Ulyanov, Vladimir V.; Shimizu, Ryoichi
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Written by well-known, award-winning authors, this is the first book to focus on high-dimensional data analysis while presenting real-world applications and research material. Emphasizing that high-dimensional asymptotic distribution can be used for a large range of samples and dimensions to achieve high levels of accuracy, this timely text provides approximation formulas, actual applications, thorough analysis of the real data, and solutions to each problem that are useful to both practical and theoretical statisticians as well as graduate students.
Wiley Series In Probability And…mehr

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Produktbeschreibung
Written by well-known, award-winning authors, this is the first book to focus on high-dimensional data analysis while presenting real-world applications and research material. Emphasizing that high-dimensional asymptotic distribution can be used for a large range of samples and dimensions to achieve high levels of accuracy, this timely text provides approximation formulas, actual applications, thorough analysis of the real data, and solutions to each problem that are useful to both practical and theoretical statisticians as well as graduate students.
Wiley Series In Probability And Statistics

Multivariate Statistics

High-Dimensionaland Large-Sample Approximations

Yasunori Fujikoshi

Vladimir V. Ulyanov

Ryoichi Shimizu

A comprehensive examination ofhigh-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.
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Autorenporträt
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.