Heijmans, Risto D.H., Pollock, D.S.G., Satorra, Albert (Eds.)
2000, XIII, 298 p.
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The three decades which have followed the publication of Heinz Neudecker's seminal paper `Some Theorems on Matrix Differentiation with Special Reference to Kronecker Products' in the Journal of theAmerican Statistical Association (1969) have witnessed the growing influence of matrix analysis in many scientific disciplines. Amongst these are the disciplines to which Neudecker has contributed directly - namely econometrics, economics, psychometrics and multivariate analysis. This book aims to illustrate how powerful the tools of matrix analysis have become as weapons in the statistician's armoury. The majority of its chapters are concerned primarily with theoretical innovations, but all of them have applications in view, and some of them contain extensive illustrations of the applied techniques. This book will provide research workers and graduate students with a cross-section of innovative work in the fields of matrix methods and multivariate statistical analysis. It should be of interest to students and practitioners in a wide range of subjects which rely upon modern methods of statistical analysis. The contributors to the book are themselves practitioners of a wide range of subjects including econometrics, psychometrics, educational statistics, computation methods and electrical engineering, but they find a common ground in the methods which are represented in the book. It is envisaged that the book will serve as an important work of reference and as a source of inspiration for some years to come.
Introduction to the Book. 1. Some Comments and a Bibliography on the Frucht-Kantorovich and Wielandt Inequalities. 2. On Matrix Trace Kantorovich-type Inequalities. 3. Matrix Inequality Applications in Econometrics. 4. On a Generalisation of the Covariance Matrix of the Multinomial Distribution. 5. A General Method of Testing for Random Parameter Variation in Statistical Models. 6. Dual Scaling and Correspondence Analysis of Rank Order Data. 7. Continuous Extensions of Matrix Formulations in Correspondence Analysis, with Applications to the FGM Family of Distributions. 8. Utility Maximisation and Mode of Payment. 9. Gibbs Sampling in B-VAR Models with Latent Variables. 10. Least-Squares Autoregression with Near-unit Root. 11. Efficiency Comparisons for a System GMM Estimator in Dynamic Panel Data Models. 12. The Rank Condition for Forward Looking Models. 13. Notes on the Elementary Properties of Permutation and Reflection Matrices. 14. S-Ancillarity and Strong Exogeneity. 15. Asymptotic Inference Based on Eigenprojections of Covariance and Correlation Matrices. 16. On a Fisher-Cornish Type Expansion of Wishart Matrices. 17. Scaled and Adjusted Restricted Tests in Multi-Sample analysis of Moment Structures. 18. Asymptotic Behaviour of Sums of Powers of Residuals in the Classic Linear Regression Model. 19. Matrix Methods for Solving Nonlinear Dynamic Optimisation Models. 20. Computers, Multilinear Algebra and Statistics. Author Index. Subject Index.