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Matrix Calculus and Zero-One Matrices - Statistical and Econometric Applications (Paperback, Revised)
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Matrix Calculus and Zero-One Matrices - Statistical and Econometric Applications (Paperback, Revised)
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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.
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