Matrix Differential Calculus with Applications in Statistics and Econometrics

MATRICES: BASIC PROPERTIES OF VECTORS AND MATRICES. Kronecker Products, the Vec Operator and the Moore-Penrose Inverse. Miscellaneous Matrix Results. DIFFERENTIALS: THE THEORY: MATHEMATICAL PRELIMINARIES. Differentials and Differentiability. The Second Differential. Static Optimization. DIFFERENTIALS: THE PRACTICE: SOME IMPORTANT DIFFERENTIALS. First Order Differentials and Jacobian Matrices. Second Order Differentials and Hessian Matrices. INEQUALITIES: INEQUALITIES. THE LINEAR MODEL: STATISTICAL PRELIMINARIES. The Linear Regression Model. Further Topics in the Linear Model. APPLICATIONS TO MAXIMUM LIKELIHOOD ESTIMATION: MAXIMUM LIKELIHOOD ESTIMATION. Simultaneous Equations. Topics in Psychometrics.