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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目次
1 | |
HighDimensional and LargeSample Approximations 2 Wishart Distribution | 29 |
HighDimensional and LargeSample Approximations 3 Hotellings T2 and Lambda Statistics | 47 |
HighDimensional and LargeSample Approximations 4 Correlation Coefficients | 69 |
HighDimensional and LargeSample Approximations 5 Asymptotic Expansions for Multivariate Basic Statistics | 91 |
HighDimensional and LargeSample Approximations 6 MANOVA Models | 149 |
HighDimensional and LargeSample Approximations 7 Multivariate Regression | 187 |
HighDimensional and LargeSample Approximations 8 Classical and HighDimensional Tests for Covariance Matrices | 219 |
HighDimensional and LargeSample Approximations 11 Canonical Correlation Analysis | 317 |
HighDimensional and LargeSample Approximations 12 Growth Curve Analysis | 349 |
HighDimensional and LargeSample Approximations 13 Approximation to the ScaleMixted Distributions | 379 |
HighDimensional and LargeSample Approximations 14 Approximation to Some Related Distributions | 423 |
HighDimensional and LargeSample Approximations 15 Error Bounds for Approximations of Multivariate Tests | 441 |
HighDimensional and LargeSample Approximations 16 Error Bounds for Approximations to Some Other Statistics | 467 |
HighDimensional and LargeSample Approximations Appendix | 495 |
513 | |
HighDimensional and LargeSample Approximations 9 Discriminant Analysis | 249 |
HighDimensional and LargeSample Approximations 10 Principal Component Analysis | 283 |