×
![]( "Buchcover ISBN 9780470539866")
„The book is designed for readers interested in multivariateanalysis with a good background in matrix algebra, mathematicalstatistical inference and probability theory. Its contents are, ingeneral, well organised and the intuitive ideas behind thedifferent multivariate methods, the asymptotic expansion techniquesand the calculation of error bounds using scale mixtures, are wellexpressed . The mathematical proofs are well presented and selectedand I have found the mathematical appendices to be very useful asguides to following the proofs.“ (Mathematical Reviews, 2011)
Multivariate Statistics
High-Dimensional and Large-Sample Approximations
von Yasunori Fujikoshi, Vladimir V. Ulyanov und Ryoichi ShimizuA 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.
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.
