Linear models and the relevant distributions and matrix algebra

Description

Content: Preface1 IntroductionLinear Statistical ModelsRegression ModelsClassificatory ModelsHierarchical Models and Random-EffectsModelsStatistical InferenceAn Overview2 Matrix Algebra: a PrimerThe BasicsPartitioned Matrices and VectorsTrace of a (Square) MatrixLinear SpacesInverse MatricesRanks and Inverses of Partitioned MatricesOrthogonalMatricesIdempotentMatricesLinear SystemsGeneralized InversesLinear Systems RevisitedProjection MatricesQuadratic FormsDeterminantsExercisesBibliographic and Supplementary Notes3 Random Vectors and MatricesExpected ValuesVariances, Covariances, and CorrelationsStandardized Version of a Random VariableConditional Expected Values and Conditional Variances and CovariancesMultivariate Normal DistributionExercisesBibliographic and Supplementary Notes4 The General Linear ModelSome Basic Types of Linear ModelsSome Specific Types of Gauss-Markov Models (With Examples)RegressionHeteroscedastic and Correlated Residual EffectsMultivariate Datavi ContentsExercisesBibliographic and Supplementary Notes5 Estimation and Prediction: Classical ApproachLinearity and UnbiasednessTranslation EquivarianceEstimabilityThe Method of Least SquaresBest LinearUnbiased or Translation-EquivariantEstimation of Estimable Functions(Under the G-M Model)Simultaneous EstimationEstimation of Variability and CovariabilityBest (Minimum-Variance) Unbiased EstimationLikelihood-Based MethodsPredictionExercisesBibliographic and Supplementary Notes6 Some Relevant Distributions and Their PropertiesChi-Square, Gamma, Beta, and Dirichlet DistributionsNoncentral Chi-Square DistributionCentral and Noncentral F DistributionsCentral, Noncentral, and Multivariate t DistributionsMoment Generating Function of the Distribution of One or More Quadratic Formsor Second-Degree Polynomials (in a Normally Distributed Random Vector)Distribution of Quadratic Forms or Second-Degree Polynomials (in a NormallyDistributed Random Vector): Chi-SquarenessThe Spectral Decomposition, With Application to the Distribution of QuadraticFormsMore on the Distribution of Quadratic Forms or Second-Degree Polynomials (in aNormally Distributed Random Vector)ExercisesBibliographic and Supplementary Notes7 Confidence Intervals (or Sets) and Tests of Hypotheses"Setting the Stage": Response Surfaces in the Context of a Specific Application andin GeneralAugmented G-M ModelThe F Test (and Corresponding Confidence Set) and the S MethodSome Optimality PropertiesOne-Sided t Tests and the Corresponding Confidence BoundsThe Residual Variance : Confidence Intervals and TestsMultiple Comparisons and Simultaneous Confidence Intervals: Some EnhancementsPredictionExercisesBibliographic and Supplementary NotesReferencesIndex