On the fundamental bordered matrix of linear estimation

Publisher Summary Many problems in economic theory, econometrics, multivariate analysis, and mathematical statistics involve the matrix, which is known as the fundamental bordered matrix of linear estimation because of its role in the Inverse Partitioned Matrix method of linear estimation. It is also called the fundamental matrix of constrained minimization because of its importance in the theory of constrained least-squares. The matrix of linear estimation also appears in the theory of optimization of definite quadratic forms under linear constraints, comparative statics analysis, and restricted maximum likelihood estimation the characterization of estimability. Very often, the matrix is known to be singular. The chapter presents properties of matrix and the Moore–Penrose (MP) inverse of matrix. The MP-inverse is unique and, therefore, has certain theoretical and pedagogical advantages over nonunique generalized inverses.

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