Heijmans / Pollock / Satorra Innovations in Multivariate Statistical Analysis

A Festschrift for Heinz Neudecker
2000
ISBN: 978-1-4615-4603-0
Verlag: Springer US
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 36, 298 Seiten, eBook

Reihe: Advanced Studies in Theoretical and Applied Econometrics

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.

Zielgruppe

Research

Autoren/Hrsg.

Heijmans, Risto D.H.

Pollock, D.S.G.

Satorra, Albert

Inhaltsverzeichnis

1 Some Comments and a Bibliography on the Frucht—Kantorovich and Wielandt Inequalities.- 1.1 Introduction and Mise-en-scène: The Frucht-Kantorovich Inequality.- 1.2 The Wielandt Inequality.- 1.3 The Schweitzer Inequality.- 1.4 The Pólya—Szegö Inequality.- 1.5 The Cassels, Krasnosel’ski?-Kre?n and Greub—Rheinboldt Inequalities.- 1.6 The Bloomfield—Watson—Knott Inequality.- 1.7 Some Other Related Inequalities.- 2 On Matrix Trace Kantorovich-type Inequalities.- 2.1 Introduction.- 2.2 Basic Inequalities.- 2.3 Mathematical Results.- 2.4 Statistical Applications.- 3 Matrix Inequality Applications in Econometrics.- 3.1 Introduction.- 3.2 Equivalent Covariance Matrices in the Multinomial Probit Model.- 3.3 Matrix Inequalities in Regression Analysis.- 3.4 A Condition for the Positivity of the MINQUE.- 3.5 Eigenvalues and Eigenvectors of a Bounded Matrix.- 3.6 Proxies and Measurement Error.- 3.7 Conclusion.- 4 On a Generalisation of the Covariance Matrix of the Multinomial Distribution.- 4.1 Introduction.- 4.2 Moore-Penrose Inverse.- 4.3 Eigenvalues.- 5 A General Method of Testing for Random Parameter Variation in Statistical Models.- 5.1 Introduction.- 5.2 Derivation of the Test.- 5.3 Examples of the Test Procedure.- 5.4 Summary.- 6 Dual Scaling and Correspondence Analysis of Rank Order Data.- 6.1 Introduction.- 6.2 Correspondence Analysis and Dual Scaling.- 6.3 Rank Order Data.- 6.4 Dual Scaling of Rank Order Data.- 6.5 Correspondence Analysis of Rank Order Data.- 6.6 Concluding Remarks.- 7 Continuous Extensions of Matrix Formulations in Correspondence Analysis, with Applications to the FGM Family of Distributions.- 7.1 Introduction.- 7.2 Discrete Correspondence Analysis.- 7.3 The Chi-square Distance.- 7.4 Continuous Random Variable Extension.- 7.5 ContinuousWeighted Metric Scaling.- 7.6 Geometric Variability, Proximity Function and Isometries.- 7.7 The FGM Family of Distributions and Correspondence Analysis.- 7.8 A Generalised FGM Family.- 8 Utility Maximisation and Mode of Payment.- 8.1 Introduction.- 8.2 Compatibility of Choice Probabilities with Stochastic Utility Max imisation.- 8.3 Choice of Mode of Payment.- 8.4 Compatibility with Utility Maximisation.- 8.5 Semiparametric Estimation of the Choice Model.- 8.6 Conclusion.- 9 Gibbs Sampling in B-VAR Models with Latent Variables.- 9.1 Introduction.- 9.2 The AR(p) Model with Latent Variables.- 9.3 The Multiple ARX(p) Model with Latent Variables.- 9.4 Further topics.- 9.5 Conclusions.- 10 Least-Squares Autoregression with Near-unit Root.- 10.1 Introduction.- 10.2 Regression without Intercept.- 10.3 Regression with Intercept.- 10.4 Negative Unit Root.- 10.5 Conclusions.- 11 Efficiency Comparisons for a System GMM Estimator in Dynamic Panel Data Models.- 11.1 Introduction.- 11.2 Model and System GMM Estimator.- 11.3 Efficiency Comparisons.- 11.4 Discussion.- 12 The Rank Condition for Forward Looking Models.- 12.1 Introduction.- 12.2 The Rank Condition.- 12.3 Hysteresis.- 12.4 Concluding Remarks.- 13 Notes on the Elementary Properties of Permutation and Re-flection Matrices.- 13.1 Introduction.- 13.2 Definitions.- 13.3 Basic Results.- 13.4 Samuelson Transformation Matrices.- 13.5 Samuelson Reflection Matrices.- 13.6 Givens Rotation Matrices.- 13.7 Eigenvalues of Permutation Matrices.- 13.8 Examples of Permutation Matrices.- 13.9 Concluding Remarks.- 14 S-Ancillarity and Strong Exogeneity.- 14.1 Introduction.- 14.2 The Main Result.- 14.3 An Example.- 15 Asymptotic Inference Based on Eigenprojections of Covariance and Correlation Matrices.- 15.1 Introduction.- 15.2 Preliminaries.- 15.3 Asymptotic Distribution of Eigenprojections.- 15.4 Testing H0 by the Chi-Square Test.- 16 On a Fisher—Cornish Type Expansion of Wishart Matrices.- 16.1 Introduction.- 16.2 The Symmetric Multivariate Normal Distribution.- 16.3 Asymptotic Approximations for Wishart Matrices.- 17 Scaled and Adjusted Restricted Tests in Multi-Sample Analysis of Moment Structures.- 17.1 Introduction.- 17.2 Goodness-of-fit tests.- 17.3 Restricted tests.- 17.4 Illustration.- 18 Asymptotic Behaviour of Sums of Powers of Residuals in the Classic Linear Regression Model.- 18.1 Introduction.- 18.2 Set-up and Main Results.- 19 Matrix Methods for Solving Nonlinear Dynamic Optimisation Models.- 19.1 Introduction.- 19.2 A Nonlinear Optimisation Framework.- 19.3 An Example.- 19.4 Summary.- 20 Computers, Multilinear Algebra and Statistics.- 20.1 Introduction.- 20.2 Problems with the Computer Screen.- 20.3 An Index Notation for the Computer Screen.- 20.4 The Index Notation Applied to Matrix Differential Calculus.- 20.5 Chain Rules.- Author Index.