Multivariate Analysis-III

List of ContributorsPrefaceAcknowledgmentsPart I/Time Series and Stochastic Processes Two-Dimensional Random Fields Preliminaries Details of the Proof of Theorem 1 References Concepts of Consistency in Spectral Estimation for Multivariate Time Series 1. Introductory Remarks 2. Should One Estimate the Spectral Distribution Function or Its Derivative? 3. Estimation of the Spectral Distribution Function F for a Multivariate Stationary Random Sequence Appendix References Non-Anticipative Canonical Representations of Equivalent Gaussian Processes 1. Introduction 2. The General Form of the Non-Anticipative Representation 3. A Derivation Using Martingale Theory 4. Concluding Remarks References Abstract Martingales and Ergodic Theory Introduction 1. The Problem 2. Martingale Formulation 3. An Operator Theoretic Approach 4. A Maximal Inequality 5. Final Remarks References On the Modelling and Estimation of Communication Channels 1. Introduction and Preliminary Discussion 2. Classes of Channels and Representations 3. Estimation of Parameters in a Linear Model 4. Channel Identification 5. Remarks References Innovation and Nonanticipative Processes 1. Innovation Processes and Regularity 2. Canonical Representations and Fully Submitted Processes ReferencesPart II/Distribution Theory and Inference Methods for Assessing Multivariate Normality 1. Introduction 2. Univariate Techniques for Evaluating Marginal Normality 3. Multivariate Techniques for Evaluating Joint Normality 4. Tests Based on Unidimensional Views of Multivariate Data 5. Examples 6. Concluding Remarks References Asymptotic Expansions for the Distributions of Characteristic Roots When the Parameter Matrix Has Several Multiple Roots 1. Introduction 2. The Maximization Procedures 3. Asymptotic Expansion for the Distribution of the Latent Roots of the Estimated Covariance Matrix-Several Multiple Population Roots 4. Asymptotic Expansion for the Distribution of the Latent Roots of S1 S21-Several Multiple Population Roots 5. Asymptotic Expansion for Manova-Several Multiple Population Roots 6. Asymptotic Expansion for Canonical Correlation-Several Multiple Population Roots 7. Complex Analogues of Previous Results 8. Remarks References Aspects of the Multinomial Logit Model 1. The General Logit Model 2. Properties of the Likelihood 3. Comment Appendix: The Beaton Sweep References Inference and Redundant Parameters 1. Introduction 2. The Probability Space Model 3. Measure Factorizations 4. If the Inner Parameter Become Known 5. A Redundant Parameter 6. The Multivariate Model 7. The Bayesian Right Invariant References The Variance Information Manifold and the Functions on It 1. The Variance Information Manifold and Its Boundary 2. The Bivariate Case 3. The Multinormal Distribution with Singular Information Matrix 4. Derivation via the Distribution of Linear Functions 5. Application to the Analysis of Experimental Designs 6. Representations as the Marginal Distribution of a Nonsingular Distribution 7. Decomposition of a Multinormal Distribution 8. Invariant Metric 9. Geodesic Distance between Two Matrices 10. Zonal Polynomials References Stopping Time in Sequential Samples from Multivariate Exponential Families 1. Introduction 2. The Main Theorem 3. Application to Examples 1.1 and 1.