Kantorovich-type inequalities and the measures of inefficiency of the glse

Abstract

In this paper we introduce some Kantorovich inequalities for the Euclidean norm of a matrix, that is, the upper bounds to ∥(X'B −1 X) −1 X'B −1 AB −1 X(X'B −1X)−1 X' BX(X'AX) −1 X'CX∥2 are given, where ∥A∥2=trace (A'A). In terms of these inequalities the upper bounds to the three measures of inefficiency of the generalized least squares estimator (GLSE) in general Gauss-Markov models are also established.