Innovations in Multivariate Statistical Analysis

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.