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Matrix Calculus and Zero-One Matrices

Statistical and Econometric Applications

Matrix Calculus and Zero-One Matrices by Darrell A. Turkington
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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.
Cambridge University Press; December 2001
220 pages; ISBN 9780511826207
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Title: Matrix Calculus and Zero-One Matrices
Author: Darrell A. Turkington