Multivariate Statistics: High-Dimensional and Large-Sample ApproximationsA 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:
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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Contents
Multivariate Normal and Related Distributions | 1 |
Wishart Distribution | 29 |
Hotellings T and Lambda Statistics | 47 |
Correlation Coefficients | 69 |
Problems | 87 |
MANOVA Models | 149 |
Classical and HighDimensional Tests for Covariance | 219 |
Discriminant Analysis | 249 |
Growth Curve Analysis | 349 |
Approximation to the ScaleMixted Distributions | 379 |
Approximation to Some Related Distributions | 423 |
Error Bounds for Approximations of Multivariate Tests | 441 |
Error Bounds for Approximations to Some Other Statistics | 467 |
Appendix | 495 |
Inequalities and MaxMin Problems | 502 |
Jacobians of Transformations | 508 |