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Matrix Differential Calculus with Applications in Statistics and Econometrics (3rd Edition) by Jan R. Magnus, Heinz Neudeckery



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Matrix Differential Calculus with Applications in Statistics and Econometrics (3rd Edition) written by Jan R. Magnus , Department of Econometrics and Operations Research, Vrije Universiteit Amsterdam, The Netherlands and Heinz Neudeckery , Amsterdam School of Economics, University of Amsterdam, The Netherlands. There has been a long-felt need for a book that gives a self-contained and unified treatment of matrix differential calculus, specifically written for econometricians and statisticians. The present book is meant to satisfy this need. It can serve as a textbook for advanced undergraduates and postgraduates in econometrics and as a reference book for practicing econometricians. Mathematical statisticians and psychometricians may also find something to their liking in the book.
When used as a textbook, it can provide a full-semester course. Reasonable proficiency in basic matrix theory is assumed, especially with the use of partitioned matrices. The basics of matrix algebra, as deemed necessary for a proper understanding of the main subject of the book, are summarized in Part One, the first of the book’s six parts. The book also contains the essentials of multivariable calculus but geared to and often phrased in terms of differentials.
The sequence in which the chapters are being read is not of great consequence. It is fully conceivable that practitioners start with Part Three (Differentials: the practice) and, dependent on their predilections, carry on to Parts Five or Six, which deal with applications. Those who want a full understanding of the underlying theory should read the whole book, although even then they could go through the necessary matrix algebra only when the specific need arises.
Matrix differential calculus as presented in this book is based on differentials, and this sets the book apart from other books in this area. The approach via differentials is, in our opinion, superior to any other existing approach. Our principal idea is that differentials are more congenial to multivariable functions as they crop up in econometrics, mathematical statistics, or psychometrics than derivatives, although from a theoretical point of view the two concepts are equivalent.

Matrix Differential Calculus with Applications in Statistics and Econometrics (3rd Edition) written by Jan R. Magnus, Heinz Neudeckery cover the following topics.

  • 1. Preface

  • Part 1 — Matrices
    2. Kronecker products, vec operator, and Moore-Penrose inverse
    3. Miscellaneous matrix results

  • Part 2 — Differentials: the theory
    4. Mathematical preliminaries
    5. Differentials and differentiability
    6. The second differential
    7. Static optimization

  • Part 3 — Differentials: the practice
    8. Some important differentials
    9. First-order differentials and Jacobian matrices
    10. Second-order differentials and Hessian matrices

  • Part 4 — Inequalities
    11. Inequalities

  • Part 5 — The linear model
    12. Statistical preliminaries
    13. The linear regression model
    14. Further topics in the linear model

  • Part 6 — Applications to maximum likelihood estimation
    15. Maximum likelihood estimation
    16. Simultaneous equations
    17. Topics in psychometrics
    18. Matrix calculus: the essentials

  • There has been a long-felt need for a book that gives a self-contained and unified treatment of matrix differential calculus, specifically written for econometricians and statisticians. The present book is meant to satisfy this need. It can serve as a textbook for advanced undergraduates and postgraduates in econometrics and as a reference book for practicing econometricians. Mathematical statisticians and psychometricians may also find something to their liking in the book. When used as a textbook, it can provide a full-semester course. Reasonable proficiency in basic matrix theory is assumed, especially with the use of partitioned matrices. The basics of matrix algebra, as deemed necessary for a proper understanding of the main subject of the book, are summarized in Part One, the first of the book’s six parts. The book also contains the essentials of multivariable calculus but geared to and often phrased in terms of differentials. The sequence in which the chapters are being read is not of great consequence. It is fully conceivable that practitioners start with Part Three (Differentials: the practice) and, dependent on their predilections, carry on to Parts Five or Six, which deal with applications. Those who want a full understanding of the underlying theory should read the whole book, although even then they could go through the necessary matrix algebra only when the specific need arises. Matrix differential calculus as presented in this book is based on differentials, and this sets the book apart from other books in this area. The approach via differentials is, in our opinion, superior to any other existing approach. Our principal idea is that differentials are more congenial to multivariable functions as they crop up in econometrics, mathematical statistics, or psychometrics than derivatives, although from a theoretical point of view the two concepts are equivalent.

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