Multivariate statistics : a vector space approach

Eaton M. Multivariate statistics.. A vector space approach (IMS, 2007)(ISBN 0940600692) Contents......Page f003.djvu Preface......Page f005.djvu Notation......Page f008.djvu 1 Vector Space Theory......Page p001.djvu 1.1 Vector Spaces......Page p002.djvu 1.2 Linear Transformations......Page p006.djvu 1.3 Inner Product Spaces......Page p013.djvu 1.4 The Cauchy-Schwarz Inequality......Page p025.djvu 1.5 The Space L(V,W)......Page p029.djvu 1.6 Determinants and Eigenvalues......Page p038.djvu 1.7 The Spectral Theorem......Page p049.djvu Problems......Page p063.djvu Notes and References......Page p069.djvu 2.1 Random Vectors......Page p070.djvu 2.2 Independence of Random Vectors......Page p076.djvu 2.3 Special Covariance Structures......Page p081.djvu Problems......Page p098.djvu Notes and References......Page p102.djvu 3 The Normal Distribution On a Vector Space......Page p103.djvu 3.1 The Normal Distribution......Page p104.djvu 3.2 Quadratic Forms......Page p109.djvu 3.3 Independence of Quadratic Forms......Page p113.djvu 3.4 Conditional Distributions......Page p116.djvu 3.5 The Density of the Normal Distribution......Page p120.djvu Problems......Page p127.djvu Notes and References......Page p131.djvu 4.1 The Classical Linear Model......Page p132.djvu 4.2 More About the Gauss-Markov Theorem......Page p140.djvu 4.3 Generalized Linear Models......Page p146.djvu Problems......Page p154.djvu Notes and References......Page p157.djvu 5.1 Matrix Factorizations......Page p159.djvu 5.2 Jacobians......Page p166.djvu Problems......Page p180.djvu Notes and References......Page p183.djvu 6 Topological Groups and Invariant Measures......Page p184.djvu 6.1 Groups......Page p185.djvu 6.2 Invariant Measures and Integrals......Page p194.djvu 6.3 Invariant Measures on Quotient Spaces......Page p207.djvu 6.4 Transformations and Factorizations of Measures......Page p218.djvu Problems......Page p228.djvu Notes and References......Page p232.djvu 7.1 Left On Invariant Distributions on n x p Matrices......Page p233.djvu 7.2 Groups Acting on Sets......Page p241.djvu 7.3 Invariant Probability Models......Page p251.djvu 7.4 The Invariance of Likelihood Methods......Page p258.djvu 7.5 Distribution Theory and Invariance......Page p267.djvu 7.6 Independence and Invariance......Page p284.djvu Problems......Page p296.djvu Notes and References......Page p299.djvu 8.1 Basic Properties......Page p302.djvu 8.2 Partitioning a Wishart Matrix......Page p309.djvu 8.3 The Noncentral Wishart Distribution......Page p316.djvu 8.4 Distributions Related to Likelihood Ratio Tests......Page p318.djvu Problems......Page p329.djvu Notes and References......Page p332.djvu 9 Inference for Means in Multivariate Linear Models......Page p334.djvu 9.1 The MANOVA Model......Page p336.djvu 9.2 MANOVA Problems with Block Diagonal Covariance Structure......Page p350.djvu 9.3 Intraclass Covariance Structure......Page p355.djvu 9.4 Symmetry Models: An Example......Page p361.djvu 9.5 Complex Covariance Structures......Page p370.djvu 9.6 Additional Examples of Linear Models......Page p381.djvu Problems......Page p397.djvu Notes and References......Page p401.djvu 10.1 Population Canonical Correlation Coefficients......Page p403.djvu 10.2 Sample Canonical Correlations......Page p419.djvu 10.3 Some Distribution Theory......Page p427.djvu 10.4 Testing for Independence......Page p443.djvu 10.5 Multivariate Regression......Page p451.djvu Problems......Page p456.djvu Notes and References......Page p463.djvu Appendix......Page p465.djvu Comments On Selected Problems......Page p471.djvu Bibliography......Page p503.djvu Index......Page p507.djvu