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Preface 1 Introduction Linear Statistical Models Regression Models Classificatory Models Hierarchical Models and Random-EffectsModels Statistical Inference An Overview 2 Matrix Algebra: a Primer The Basics Partitioned Matrices and Vectors Trace of a (Square) Matrix Linear Spaces Inverse Matrices Ranks and Inverses of Partitioned Matrices OrthogonalMatrices IdempotentMatrices Linear Systems Generalized Inverses Linear Systems Revisited Projection Matrices Quadratic Forms Determinants Exercises Bibliographic and Supplementary Notes 3 Random Vectors and Matrices Expected Values Variances, Covariances, and Correlations Standardized Version of a Random Variable Conditional Expected Values and Conditional Variances and Covariances Multivariate Normal Distribution Exercises Bibliographic and Supplementary Notes 4 The General Linear Model Some Basic Types of Linear Models Some Specific Types of Gauss-Markov Models (With Examples) Regression Heteroscedastic and Correlated Residual Effects Multivariate Data vi Contents Exercises Bibliographic and Supplementary Notes 5 Estimation and Prediction: Classical Approach Linearity and Unbiasedness Translation Equivariance Estimability The Method of Least Squares Best LinearUnbiased or Translation-EquivariantEstimation of Estimable Functions (Under the G-M Model) Simultaneous Estimation Estimation of Variability and Covariability Best (Minimum-Variance) Unbiased Estimation Likelihood-Based Methods Prediction Exercises Bibliographic and Supplementary Notes 6 Some Relevant Distributions and Their Properties Chi-Square, Gamma, Beta, and Dirichlet Distributions Noncentral Chi-Square Distribution Central and Noncentral F Distributions Central, Noncentral, and Multivariate t Distributions Moment Generating Function of the Distribution of One or More Quadratic Forms or Second-Degree Polynomials (in a Normally Distributed Random Vector) Distribution of Quadratic Forms or Second-Degree Polynomials (in a Normally Distributed Random Vector): Chi-Squareness The Spectral Decomposition, With Application to the Distribution of Quadratic Forms More on the Distribution of Quadratic Forms or Second-Degree Polynomials (in a Normally Distributed Random Vector) Exercises Bibliographic and Supplementary Notes 7 Confidence Intervals (or Sets) and Tests of Hypotheses "Setting the Stage": Response Surfaces in the Context of a Specific Application and in General Augmented G-M Model The F Test (and Corresponding Confidence Set) and the S Method Some Optimality Properties One-Sided t Tests and the Corresponding Confidence Bounds The Residual Variance : Confidence Intervals and Tests Multiple Comparisons and Simultaneous Confidence Intervals: Some Enhancements Prediction Exercises Bibliographic and Supplementary Notes References Index