A survey of Cauchy-Schwarz and Kantorovich-type matrix inequalities

DOI10.1007/BF02927110zbMath0915.62056OpenAlexW2068945207MaRDI QIDQ1280036

Shuangzhe Liu, Heinz Neudecker

Publication date: 18 May 1999

Published in: Statistical Papers (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02927110

zbMATH Keywords

Kantorovich inequalitiesCauchy-Schwarz inequalities

Mathematics Subject Classification ID

Applications of statistics to economics (62P20) Multivariate analysis (62H99) Miscellaneous inequalities involving matrices (15A45)

Related Items (3)

Matrix Euclidean norm Wielandt inequalities and their applications to statistics ⋮ Matrix trace Wielandt inequalities with statistical applications ⋮ Matrix differential calculus with applications in the multivariate linear model and its diagnostics

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Generalized matrix versions of the Cauchy-Schwarz and Kantorovich inequalities
• Matrix versions of the Cauchy and Kantorovich inequalities
• The inefficiency of least squares: Extensions of the Kantorovich inequality
• Some extensions of the Kantorovich inequality and statistical applications
• Bounds for the trace of the difference of the covariance matrices of the OLSE and BLUE
• Kantorovich and Cauchy-Schwarz inequalities involving positive semidefinite matrices, and efficiency comparisons for a singular linear model
• Some comments on six inequalities associated with the inefficiency of ordinary least squares with one regressor
• Some further matrix extensions of the Cauchy-Schwarz and Kantorovich inequalities, with some statistical applications
• Several matrix Kantorovich-type inequalities
• A matrix inequality including that of Kantorovich
• Some matrix inequalities
• The inefficiency of least squares
• A matrix version of the Ky Fan generalization of the kantorovich inequality
• Kantorovich inequalities and efficiency comparisons for several classes of estimators in linear models
• Differences of means
• Comparison of the Variance of Minimum Variance and Weighted Least Squares Regression Coefficients
• Comparison of Least Squares and Minimum Variance Estimates of Regression Parameters
• Inequalities: theory of majorization and its applications

This page was built for publication: A survey of Cauchy-Schwarz and Kantorovich-type matrix inequalities