Generalized Vectorization, Cross-Products, and Matrix Calculus

by Darrell A. Turkington

Overview

This book presents the reader with new operators and matrices that arise in the area of matrix calculus. The properties of these mathematical concepts are investigated and linked with zero-one matrices such as the commutation matrix. Elimination and duplication matrices are revisited and partitioned into submatrices. Studying the properties of these submatrices facilitates achieving new results for the original matrices themselves. Different concepts of matrix derivatives are presented and transformation principles linking these concepts are obtained. One of these concepts is used to derive new matrix calculus results, some involving the new operators and others the derivatives of the operators themselves. The last chapter contains applications of matrix calculus, including optimization, differentiation of log-likelihood functions, iterative interpretations of maximum likelihood estimators, and a Lagrangian multiplier test for endogeneity.

Product Details

ISBN-13:	9781107032002
Publisher:	Cambridge University Press
Publication date:	02/11/2013
Pages:	275
Product dimensions:	6.14(w) x 9.25(h) x 0.75(d)

About the Author

Darrell A. Turkington is a Professor of Economics at the University of Western Australia. His numerous publications include articles in leading international journals such as the Journal of the American Statistical Association, the International Economic Review and the Journal of Econometrics. He is also the author of Instrumental Variables (Cambridge University Press, 1985, with Roger J. Bowden), Matrix Calculus and Zero-One Matrices: Statistical and Econometric Applications (Cambridge University Press, 2002) and Mathematical Tools for Economics (2007). Professor Turkington received his Ph.D. in theoretical economics from the University of California, Berkeley.

Table of Contents

1. Mathematical prerequisites; 2. Zero-one matrices; 3. Elimination and duplication matrices; 4. Matrix calculus; 5. New matrix calculus results; 6. Applications.

What People are Saying About This

From the Publisher

Advance praise: 'A very neat treatment of matrix calculus. There is no doubt that the new operators and matrices presented in the book will see their applications in many areas of econometrics.' Yong Bao, Purdue University

'This book is very clearly written in a text style that conveys what needs to be said with no superfluous discussion. It represents a substantial contribution to our understanding of a difficult area. It is a beautiful book, and destined to become a classic.' Ross Maller, Australian National University

Editorial Reviews

'A very neat treatment of matrix calculus. There is no doubt that the new operators and matrices presented in the book will see their applications in many areas of econometrics.' Yong Bao, Purdue University

'This book is very clearly written in a text style that conveys what needs to be said with no superfluous discussion. It represents a substantial contribution to our understanding of a difficult area. It is a beautiful book, and destined to become a classic.' Ross Maller, Australian National University

From the Publisher