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

Kantorovich-type inequalities and the measures of inefficiency of the glse 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

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

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Publisher
Springer Journals
Copyright
Copyright © 1989 by Science Press, Beijing, China and Allerton Press, Inc., New York, U.S.A.
Subject
Mathematics; Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/BF02005959
Publisher site
See Article on Publisher Site

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.

Journal

Acta Mathematicae Applicatae SinicaSpringer Journals

Published: Jul 13, 2005

References