Matrix calculus and zero-one matrices : statistical and econometric applications

Machine generated contents note: 1 Classical Statistical Procedures -- 1.1 Introduction -- 1.2 The Score Vector, the Information Matrix, and the Cramer-Rao -- Lower Bound -- 1.3 Maximum Likelihood Estimators and Test Procedures -- 1.4 Nuisance Parameters -- 1.5 Differentiation and Asymptotics -- 2 Elements of Matrix Algebra -- 2.1 Introduction -- 2.2 Kronecker Products -- 2.3 The Vec and the Devec Operators -- 2.4 Generalized Vec and Devec Operators -- 2.5 Triangular Matrices and Band Matrices -- 3 Zero-One Matrices -- 3.1 Introduction -- 3.2 Selection Matrices and Permutation Matrices -- 3.3 The Commutation Matrix and Generalized Vecs and Devecs of -- the Commutation Matrix -- 3.4 Elimination-Matrices L, L -- 3.5 Duplication Matrices D, L' -- 3.6 Results Concerning Zero-One Matrices Associated with an -- n x n Matrix -- 3.7 Shifting Matrices -- 4 Matrix Calculus -- 4.1 Introduction -- 4.2 Basic Definitions -- 4.3 Some Simple Matrix Calculus Results -- 4.4 Matrix Calculus and Zero-One Matrices -- 4.5 The Chain Rule and the Product Rule for Matrix Calculus -- 4.6 Rules for Vecs of Matrices -- 4.7 Rules Developed from the Properties of KGn, K n, and Knr -- 4.8 Rules for Scalar Functions of a Matrix -- 4.9 Tables of Results -- 5 Linear-Regression Models -- 5.1 Introduction -- 5.2 The Basic Linear-Regression Model -- 5.3 The Linear-Regression Model with -- Autoregressive Disturbances -- 5.4 Linear-Regression Model with Moving-Average Disturbances -- Appendix 5.A Probability Limits Associated with the -- Information Matrix for the Autoregressive Disturbances Model, -- Appendix 5.B Probability Limits Associated with the -- Information Matrix for the Moving-Average Disturbances -- Model -- 6 Seemingly Unrelated Regression Equations Models -- 6.1 Introduction -- 6.2 The Standard SURE Model -- 6.3 The SURE Model with Vector Autoregressive Disturbances -- 6.4 The SURE Model with Vector Moving-Average Disturbances -- Appendix 6.A Probability Limits Associated with the -- Information Matrix of the Model with Moving-Average -- Disturbances -- 7 Linear Simultaneous Equations Models -- 7.1 Introduction -- 7.2 The Standard Linear Simultaneous Equations Model -- 7.3 The Linear Simultaneous Equations Model with Vector -- Autoregressive Disturbances -- 7.4 The Linear Simultaneous Equations Model with Vector -- Moving-Average Disturbances -- Appendix 7.A Consistency of R and S -- References and Suggested Readings -- Index