Matrix Differential Calculus with Applications in Statistics and Econometrics, 3rd Edition

✍ Scribed by Jan R. Magnus, Heinz Neudecker

• Publisher: Wiley
• Year: 2007
• Tongue: English
• Leaves: 470
• Edition: Rev Sub
• Category: Library

✦ Synopsis

This text is a self-contained and unified treatment of matrix differential calculus, specifically written for econometricians and statisticians. It can serve as a textbook for advanced undergraduates and postgraduates in econometrics and as a reference book for practising econometricians.

✦ Table of Contents

Front Cover......Page 1
Back Cover......Page 2
Contents......Page 7
Preface......Page 15
Part One - Matrices......Page 21
1. Basic properties of vectors and matrices......Page 23
2. Kronecker products, the vec operator and the Moore-Penrose inverse......Page 51
3. Miscellaneous matrix results......Page 67
Part Two - Differentials: the theory......Page 93
4. Mathematical preliminaries......Page 95
5. Differentials and differentiability......Page 109
6. The second differential......Page 133
7. Static optimization......Page 153
Part Three - Differentials: the practice......Page 185
8. Some important differentials......Page 187
9. First-order differentials and Jacobian matrices......Page 213
10. Second-order differentials and Hessian matrices......Page 233
Part Four - Inequalities......Page 243
11. Inequalities......Page 245
Part Five - The linear model......Page 293
12. Statistical preliminaries......Page 295
13. The linear regressional model......Page 307
14. Further topics in the linear model......Page 343
Part Six - Applications to maximum likelihood estimation......Page 369
15. Maximum likelihood estimation......Page 371
16. Simultaneous equations......Page 391
17. Topics in psychometrics......Page 415
Bibliography......Page 447
Index of symbols......Page 459
Subject index......Page 463