Matrix Calculus and Zero-One Matrices: Statistical and Econometric Applications
Cambridge University Press, 4/11/2002
EAN 9780521807883, ISBN10: 0521807883
Hardcover, 220 pages, 22.9 x 15.2 x 1.6 cm
Language: English
This 2002 book presents the reader with mathematical tools taken from matrix calculus and zero-one matrices and demonstrates how these tools greatly facilitate the application of classical statistical procedures to econometric models. The matrix calculus results are derived from a few basic rules that are generalizations of the rules of ordinary calculus. These results are summarized in a useful table. Well-known zero-one matrices, together with some newer ones, are defined, their mathematical roles explained, and their useful properties presented. The basic building blocks of classical statistics, namely the score vector, the information matrix, and the Cramer-Rao lower bound, are obtained for a sequence of linear econometric models of increasing statistical complexity. From these are obtained interactive interpretations of maximum likelihood estimators, linking them with efficient econometric estimators. Classical test statistics are also derived and compared for hypotheses of interest.
1. Classical statistical procedures
2. Elements of matrix algebra
3. Zero-one matrices
4. Matrix calculus
5. Linear regression models
6. Seemingly unrelated regression equations models
7. Linear simultaneous equations models.
‘This is indeed a fine book covering the major areas in the Econometric literature. … The book, with its lucid presentation, will be quite valuable as a reference book for instructors as well as graduate students.‘ Indian Journal of Statistics