Matrix Differential Calculus with Applications in Statistics and Econometrics

Matrix Differential Calculus With Applications in Statistics and Econometrics Revised Edition Jan R. Magnus, CentER, Tilburg University, The Netherlands and Heinz Neudecker, Cesaro, Schagen, The Netherlands " .deals rigorously with many of the problems that have bedevilled the subject up to the present time." - Stephen Pollock, Econometric Theory "I continued to be pleasantly surprised by the variety and usefulness of its contents " - Isabella Verdinelli, Journal of the American Statistical Association Continuing the success of their first edition, Magnus and Neudecker present an exhaustive and self-contained revised text on matrix theory and matrix differential calculus. Matrix calculus has become an essential tool for quantitative methods in a large number of applications, ranging from social and behavioural sciences to econometrics. While the structure and successful elements of the first edition remain, this revised and updated edition contains many new examples and exercises.
* Contains the essentials of multivariable calculus with an emphasis on the use of differentials
* Many new examples and exercises
* Fulfils the need for a unified and self-contained treatment of matrix differential calculus
* Includes new developments in this field
Part I presents a concise, yet thorough overview of matrix algebra, while the second part develops the theory of differentials. The remaining Parts III to VI combine the theory and application of matrix differential calculus providing the practitioner and researcher with both a quick review and a detailed reference. Visit our web page http://www.wiley.com/Ein umfassendes Lehrbuch der Matrixdifferentialrechnung für Statistiker und Ökonometriker, in deren Forschungsalltag die Matrixtheorie eine zentrale Rolle spielt. Gegenüber der hervorragend aufgenommenen ersten Auflage haben die Autoren, anerkannte Experten dieses Gebietes, den Text um neue Entwicklungen erweitert; die Beispiele und Übungsaufgaben wurden ebenfalls ergänzt. (06/99)

Preface xv

Preface to the first revised printing xvii

Preface to the second revised printing xviii

Part One- Matrices

Part Two- Differentials: the theory

Part Three- Differentials: the practice

Part Four- Inequalities

Part Five- The linear model

Part Six- Applications to maximum likelihood estimation

Bibliography 379

Index of Symbols 387

Subject Index 390

"...the best book to learn matrix and related ideas...statisticians, econometricians, computer scientists, engineers, and psychometricians will find this extremely useful." (Journal of Statistical Computation and Simulation, March 2006)

"a most welcome revision" (Computational Statistics & Data Analysis, 28 August 2001)

Jan R. Magnus is the author of Matrix Differential Calculus with Applications in Statistics and Econometrics, 2nd Edition, published by Wiley. Heinz Neudecker is the author of Matrix Differential Calculus with Applications in Statistics and Econometrics, 2nd Edition, published by Wiley. " ...deals rigorously with many of the problems that have bedevilled the subject up to the present time..." - Stephen Pollock, Econometric Theory

"I continued to be pleasantly surprised by the variety and usefulness of its contents " - Isabella Verdinelli, Journal of the American Statistical Association

Continuing the success of their first edition, Magnus and Neudecker present an exhaustive and self-contained revised text on matrix theory and matrix differential calculus. Matrix calculus has become an essential tool for quantitative methods in a large number of applications, ranging from social and behavioural sciences to econometrics. While the structure and successful elements of the first edition remain, this revised and updated edition contains many new examples and exercises.
* Contains the essentials of multivariable calculus with an emphasis on the use of differentials
* Many new examples and exercises
* Fulfils the need for a unified and self-contained treatment of matrix differential calculus
* Includes new developments in this field
Part I presents a concise, yet thorough overview of matrix algebra, while the second part develops the theory of differentials. The remaining Parts III to VI combine the theory and application of matrix differential calculus providing the practitioner and researcher with both a quick review and a detailed reference.