Matrix Differential Calculus with Applications in Statistics and Econometrics

ISBN-13: 9780471986331 / Angielski / Miękka / 1999 / 432 str.

Jan R. Magnus; Heinz Neudecker; H. Neudecker

Opis

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/

Recenzje

" 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)

Spis treści

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.

Blurb

"...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.