Multivariate Statistical Inference

PrefaceAcknowledgmentsChapter I Vector and Matrix Algebra 1.0 Introduction 1.1 Vectors 1.2 Matrices 1.3 Rank and Trace of a Matrix 1.4 Quadratic Forms and Positive Definite Matrix 1.5 Characteristic Roots and Vectors 1.6 Partitioned Matrix 1.7 Some Special Theorems 1.8 Complex Matrices Exercises ReferencesChapter II Groups and Jacobian of Some Transformations 2.0 Introduction 2.1 Groups 2.2 Some Examples of Groups 2.3 Normal Subgroups, Quotient Group, Homomorphism, Isomorphism, Direct Product 2.4 Jacobian of Some Transformations Further ReadingChapter III Notions of Multivariate Distributions and Invariance in Statistical Inference 3.0 Introduction 3.1 Multivariate Distributions 3.2 Invariance in Statistical Testing of Hypotheses 3.3 Sufficiency and Invariance 3.4 Unbiasedness and Invariance 3.5 Invariance and Optimum Tests 3.6 Most Stringent Tests and Invariance Exercises ReferencesChapter IV Multivariate Normal Distribution, Its Properties and Characterization 4.0 Introduction 4.1 Multivariate Normal Distribution (Classical Approach) 4.2 Some Characterizations of the Normal Distribution 4.3 Complex Multivariate Normal Distribution 4.4 Concentration Ellipsoid and Axes 4.5 Some Examples 4.6 Regression, Multiple and Partial Correlation Exercises ReferencesChapter V Estimators of Parameters and Their Functions in a Multivariate Normal Distribution 5.0 Introduction 5.1 Maximum Likelihood Estimators of µ, S 5.2 Properties of Maximum Likelihood Estimators of µ and S 5.3 Bayes, Minimax, and Admissible Characters of the Maximum Likelihood Estimator of µ, S Exercises ReferencesChapter VI Basic Multivariate Sampling Distributions 6.0 Introduction 6.1 Noncentral Chi-Square, Student's t-, F-Distributions 6.2 Distribution of Quadratic Forms, Cochran's Theorem 6.3 The Wishart Distribution 6.4 Tensor Product, Properties of the Wishart Distribution 6.5 The Noncentral Wishart Distribution 6.6 Generalized Variance 6.7 Distribution of the Bartlett Decomposition (Rectangular Coordinates) 6.8 Distribution of Hotelling's T2 and a Related Distribution 6.9 Distribution of Multiple and Partial Correlation Coefficients Exercises ReferencesChapter VII Tests of Hypotheses of Mean Vectors 7.0 Introduction 7.1 Tests and Confidence Region for Mean Vectors with Known Covariance Matrices 7.2 Tests and Confidence Region for Mean Vectors with Unknown Covariance Matrices 7.3 Tests of Hypotheses Concerning Subvectors of µ Exercises ReferencesChapter VIII Tests Concerning Covariance Matrices and Mean Vectors 8.0 Introduction 8.1 Hypothesis that a Covariance Matrix is Equal to a Given Matrix 8.2 The Sphericity Test 8.3 Tests of Independence and the R2-Test 8.4 Multivariate General Linear Hypothesis 8.5 Equality of Several Covariance Matrices Exercises ReferencesChapter IX Discriminant Analysis 9.0 Introduction 9.1 Examples 9.2 Formulation of the Problem of Discriminant Analysis 9.3 Classification into One of Two Multivariate Normal Populations 9.4 Classification into More than Two Multivariate Normal Populations 9.5 Concluding Remarks Exercises ReferencesChapter X Multivariate Covariance Models 10.0 Introduction 10.1 Principal Components 10.2 Factor Analysis 10.3 Canonical Correlations 10.4 Time Series Analysis Exercises ReferencesIndexes