This book provides a unified treatment of matrix differential calculus, specifically written for econometricians and statisticians. Divided into six parts, the book begins with a treatment of matrix algebra, discussing the Schur, Jordan, and singular-value decompositions, the Hadamard and Kronecker products, and more. The second section is the theoretical core of the book and presents a thorough development of the theory of differentials. Practically-oriented, part three contains the rules for working with differentials and lists the differentials of important scalar, vector, and matrix functions. The fourth deals with inequalities, such as Cauchy-Schwarz's and Minkowski's, while the fifth section is devoted to applications of matrix differential calculus to the linear regression model. The book closes by detailing maximum likelihood estimation, an ideal source for demonstrating the power of the propagated techniques. Features numerous exercises.
|Series:||Wiley Series in Probability and Statistics - Applied Probability and Statistics Section Series , #231|
|Product dimensions:||6.30(w) x 9.33(h) x 1.02(d)|
Table of Contents
Basic Properties of Vectors and Matrices.
Kronecker Products, the Vec-Operator, and the Moore-Penrose Inverse.
Miscellaneous Matrix Results.
DIFFERENTIALS: THE THEORY.
Differentials and Differentiability.
The Second Differential.
DIFFERENTIALS: THE PRACTICE.
Some Important Differentials.
First-Order Differentials and Jacobian Matrices.
Second-Order Differentials and Hessian Matrices.
THE LINEAR MODEL.
The Linear Regression Model.
Further Topics in the Linear Model.
APPLICATIONS TO MAXIMUM LIKELIHOOD ESTIMATION.
Maximum Likelihood Estimation.
Topics in Psychometrics.