Matrix differential calculus with applications in statistics and econometrics
著者
書誌事項
Matrix differential calculus with applications in statistics and econometrics
（Wiley series in probability and mathematical statistics, . Applied probability and statistics）
Wiley, c1988
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注記
Includes bibliographies and indexes
内容説明・目次
内容説明
This book provides a self-contained and unified treatment of matrix differential calculus, aimed at econometricians and statisticians. It can be used as a textbook for senior undergraduate or graduate courses on the subject, and will also be a valuable source for professional econometricians and statisticians who want to learn and apply these important techniques. The authors base their approach on differentials rather than derivatives, and they show that the use of differentials is elegant, easy and considerably more useful in applications. No specialist knowledge of matrix algebra or calculus is required, since the basics of matrix algebra are covered in the first three chapters with a thorough treatment of multivariable calculus provided in Chapters Four to Seven. Exercises are included in each chapter, and many examples which illustrate applications of the theory are considered in detail.
目次
- Preface
- 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
- Subject Index
- Bibliography.
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