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Published in: Journal of Inequalities and Applications 1/2009

Open Access 01-12-2009 | Research Article

Several Matrix Euclidean Norm Inequalities Involving Kantorovich Inequality

Authors: Litong Wang, Hu Yang

Published in: Journal of Inequalities and Applications | Issue 1/2009

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Abstract

Kantorovich inequality is a very useful tool to study the inefficiency of the ordinary least-squares estimate with one regressor. When regressors are more than one statisticians have to extend it. Matrix, determinant, and trace versions of it have been presented in the literature. In this paper, we provide matrix Euclidean norm Kantorovich inequalities.

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Literature
1.
go back to reference Watson GS: Serial correlation in regression analysis, Ph.D. thesis. Department of Experimental Statistics, North Carolina State College, Raleigh, NC, USA; 1951. Watson GS: Serial correlation in regression analysis, Ph.D. thesis. Department of Experimental Statistics, North Carolina State College, Raleigh, NC, USA; 1951.
2.
go back to reference Watson GS, Alpargu G, Styan GPH: Some comments on six inequalities associated with the inefficiency of ordinary least squares with one regressor. Linear Algebra and Its Applications 1997, 264: 13–54.MathSciNetCrossRefMATH Watson GS, Alpargu G, Styan GPH: Some comments on six inequalities associated with the inefficiency of ordinary least squares with one regressor. Linear Algebra and Its Applications 1997, 264: 13–54.MathSciNetCrossRefMATH
3.
go back to reference Drury SW, Liu S, Lu C-Y, Puntanen S, Styan GPH: Some comments on several matrix inequalities with applications to canonical correlations: historical background and recent developments. Sankhyā 2002,64(2):453–507.MathSciNetMATH Drury SW, Liu S, Lu C-Y, Puntanen S, Styan GPH: Some comments on several matrix inequalities with applications to canonical correlations: historical background and recent developments. Sankhyā 2002,64(2):453–507.MathSciNetMATH
4.
go back to reference Marshall AW, Olkin I: Multivariate distributions generated from mixtures of convolution and product families. In Topics in Statistical Dependence (Somerset, PA, 1987), Ims Lecture Notes-Monograph Series. Volume 16. Institute of Mathematical Statistics, Hayward, Calif, USA; 1990:371–393. Marshall AW, Olkin I: Multivariate distributions generated from mixtures of convolution and product families. In Topics in Statistical Dependence (Somerset, PA, 1987), Ims Lecture Notes-Monograph Series. Volume 16. Institute of Mathematical Statistics, Hayward, Calif, USA; 1990:371–393.
5.
go back to reference Wang SG, Jia ZZ: Matrix Inequalities. Science Press, Beijing, China; 1994. Wang SG, Jia ZZ: Matrix Inequalities. Science Press, Beijing, China; 1994.
8.
go back to reference Yang H: Extensions of the Kantorovich inequality and the error ratio efficiency of the mean square. Mathematica Applicata 1988,1(4):85–90.MathSciNetMATH Yang H: Extensions of the Kantorovich inequality and the error ratio efficiency of the mean square. Mathematica Applicata 1988,1(4):85–90.MathSciNetMATH
9.
go back to reference Greub W, Rheinboldt W: On a generalization of an inequality of L. V. Kantorovich. Proceedings of the American Mathematical Society 1959, 10: 407–415. 10.1090/S0002-9939-1959-0105028-3MathSciNetCrossRefMATH Greub W, Rheinboldt W: On a generalization of an inequality of L. V. Kantorovich. Proceedings of the American Mathematical Society 1959, 10: 407–415. 10.1090/S0002-9939-1959-0105028-3MathSciNetCrossRefMATH
10.
go back to reference Yang H, Wang L: An alternative form of the Watson efficiency. Journal of Statistical Planning and Inference 2009,139(8):2767–2774. 10.1016/j.jspi.2009.01.002MathSciNetCrossRefMATH Yang H, Wang L: An alternative form of the Watson efficiency. Journal of Statistical Planning and Inference 2009,139(8):2767–2774. 10.1016/j.jspi.2009.01.002MathSciNetCrossRefMATH
Metadata
Title
Several Matrix Euclidean Norm Inequalities Involving Kantorovich Inequality
Authors
Litong Wang
Hu Yang
Publication date
01-12-2009
Publisher
Springer International Publishing
Published in
Journal of Inequalities and Applications / Issue 1/2009
Electronic ISSN: 1029-242X
DOI
https://doi.org/10.1155/2009/291984

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