Matrix Calculus and Zero-One Matrices: Statistical and Econometric Applications

This presents the reader with mathematical tools taken from matrix calculus and zero-one matrices and demonstrates how these tools facilitate the application of classical statistical procedures to econometric models. The matrix calculus results are derived from basic rules which are generalizations of the rules of ordinary calculus. These results are summarized in a table. Well-known zero-one matrices together with some new ones are defined, their mathematical roles explained and their 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 statistical complexity. From these interactive interpretations of maximum likelihood estimators are obtained linking them with efficient econometric estimators. Classical test statistics are also derived and compared for hypotheses of interest.