SUMMARY Five extensions of the classical two-set theory of canonical correlation analysis to three or more sets are considered. For each one, a model of the general principal component type is constructed to aid in motivating, comparing and understanding the methods. Procedures are developed for finding the canonical variables associated with the different approaches. Some practical considerations and an example are also included.

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Canonical analysis of several sets of variables

A comprehensive, must-have handbook of matrix methods with a unique emphasis on statistical applications This timely book, A Matrix Handbook for Statisticians, provides a comprehensive, encyclopedic treatment of matrices as they relate to both statistical concepts and methodologies. Written by an experienced authority on matrices and statistical theory, this handbook is organized by topic rather than mathematical developments and includes numerous references to both the theory behind the methods and the applications of the methods. A uniform approach is applied to each chapter, which contains four parts: a definition followed by a list of results; a short list of references to related topics in the book; one or more references to proofs; and references to applications. The use of extensive cross-referencing to topics within the book and external referencing to proofs allows for definitions to be located easily as well as interrelationships among subject areas to be recognized. A Matrix Handbook for Statisticians addresses the need for matrix theory topics to be presented together in one book and features a collection of topics not found elsewhere under one cover. These topics include: * Complex matrices * A wide range of special matrices and their properties * Special products and operators, such as the Kronecker product * Partitioned and patterned matrices * Matrix analysis and approximation * Matrix optimization * Majorization * Random vectors and matrices * Inequalities, such as probabilistic inequalities Additional topics, such as rank, eigenvalues, determinants, norms, generalized inverses, linear and quadratic equations, differentiation, and Jacobians, are also included. The book assumes a fundamental knowledge of vectors and matrices, maintains a reasonable level of abstraction when appropriate, and provides a comprehensive compendium of linear algebra results with use or potential use in statistics. A Matrix Handbook for Statisticians is an essential, one-of-a-kind book for graduate-level courses in advanced statistical studies including linear and nonlinear models, multivariate analysis, and statistical computing. It also serves as an excellent self-study guide for statistical researchers.

A matrix handbook for statisticians

Preface Introduction One Sample A General Theory for Testing and Confidence Intervals Two Sample Problems One-Way Analysis of Variance Multiple Comparison Methods Simple Linear and Polynomial Regression The Analysis of Count Data Basic Experimental Designs Analysis of Covariance Factorial Treatment Structures Split Plots, Repeated Measures, Random Effects, and Subsampling Multiple Regression: Matrix Formation Unbalanced Multifactor Analysis of Variance Confounding and Fractional Replication in 2n Factorial Systems Nonlinear Regression Appendix A: Matrices Appendix B: Tables References Author Index Subject Index

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Analysis of Variance, Design, and Regression: Applied Statistical Methods

Two proposals are made that may facilitate the creation of derivative market instruments, such as futures contracts, cash settled based on economic indices. The first proposal concerns index number construction: indices based on infrequent measurements of nonstandardized items may control for quality change by using a hedonic repeated measures method, an index number construction method that follows individual assets or subjects through time and also takes account of measured quality variables. The second proposal is to establish markets for perpetual claims on cash flows matching indices of dividends or rents. Such markets may help us to measure the prices of the assets generating these dividends or rents even when the underlying asset prices are difficult or impossible to observe directly. A perpetual futures contract is proposed that would cash settle every day in terms of both the change in the futures price and the dividend or rent index for that day. THIS PAPER CONCERNS PROBLEMS in the measurement of asset values or present values, problems that, if solved, may facilitate the creation of new hedging vehicles, new cash-settled futures, options, and other derivative financial products. The greatest components of world wealth are not hedgeable at all, and

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Measuring Asset Values for Cash Settlement in Derivative Markets: Hedonic Repeated Measures Indices and Perpetual Futures

Separation theorems for singular values of matrices and their applications in multivariate analysis

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Masashi Okamoto

Papers

Minimization of Eigenvalues of a Matrix and Optimality of Principal Components