Read more
Zusatztext "a most welcome revision"(Computational Statistics & Data Analysis! 28 August 2001) Informationen zum Autor 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. Klappentext " ...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. Zusammenfassung Matrix calculus has become an essential tool for quantitative methods in a large number of applications, ranging from social and behavioral sciences to econometrics. 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. Inhaltsverzeichnis 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 ...
List of contents
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.
Report
"...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)
