Matrix Calculus and Zero-One Matrices

Statistical and Econometric Applications
Erscheinungsjahr 2011
ISBN: 978-0-521-80788-3
Verlag: Cambridge University Press

Buch, Englisch, 218 Seiten, Format (B × H): 157 mm x 235 mm, Gewicht: 515 g

This 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 new 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.

Autoren/Hrsg.

Turkington, Darrell A.

Fachgebiete

• Wirtschaftswissenschaften Volkswirtschaftslehre Volkswirtschaftslehre Allgemein Ökonometrie
• Mathematik | Informatik Mathematik Algebra Homologische Algebra
• Wirtschaftswissenschaften Betriebswirtschaft Wirtschaftsmathematik und -statistik

Inhaltsverzeichnis

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.