Some extensions of the Kantorovich inequality and statistical applications

DOI10.1016/0047-259X(81)90092-0zbMath0482.15010MaRDI QIDQ1162561

C. Radhakrishna Rao, Chinubal G. Khatri

Publication date: 1981

Published in: Journal of Multivariate Analysis (Search for Journal in Brave)

zbMATH Keywords

upper boundeigenvaluessingular valuespositive definite matrixtracesinequality of Kantorovichleast squares theory of estimationproduct of determinantsproduct of two quadratic forms

Mathematics Subject Classification ID

Linear regression; mixed models (62J05) Determinants, permanents, traces, other special matrix functions (15A15) Inequalities involving eigenvalues and eigenvectors (15A42) Eigenvalues, singular values, and eigenvectors (15A18) Quadratic and bilinear forms, inner products (15A63)

Related Items (20)

The inefficiency of least squares: Extensions of the Kantorovich inequality ⋮ Some Matrix Norm Kantorovich Inequalities and Their Applications ⋮ A brief proof on the generalized variance bound of the relative efficiency in statistics ⋮ Matrix norm versions of the Kantorovich inequality and its applications ⋮ Kantorovich and Cauchy-Schwarz inequalities involving positive semidefinite matrices, and efficiency comparisons for a singular linear model ⋮ A brief biography and appreciation of Calyampudi Radhakrishna Rao, with a bibliography of his books and papers ⋮ A refined efficiency rate for ordinary least squares and generalized least squares estimators for a linear trend with autoregressive errors ⋮ Extrema of quadratic forms and statistical applications ⋮ On the measures of multicollinearity in least squares regression ⋮ Refinements of Kantorovich inequality for Hermitian matrices ⋮ Unnamed Item ⋮ Kantorovich-type inequalities and the measures of inefficiency of the GLSE ⋮ New inequalities of the Kantorovich type for bounded linear operators in Hilbert spaces ⋮ Efficiency comparisons between the OLSE and the BLUE in a singular linear model ⋮ The inefficiency of the least squares estimator and its bound ⋮ Constrained Kantorovich inequalities and relative efficiency of least squares ⋮ Convexity conditions of Kantorovich function and related semi-infinite linear matrix inequalities ⋮ An alternative form of the Watson efficiency ⋮ Matrix differential calculus with applications in the multivariate linear model and its diagnostics ⋮ A survey of Cauchy-Schwarz and Kantorovich-type matrix inequalities

Cites Work

• Separation theorems for singular values of matrices and their applications in multivariate analysis
• On a Generalization of an Inequality of L. V. Kantorovich
• On the Kantorovich Inequality
• The inefficiency of least squares
• On the minimum efficiency of least squares
• Linear Statistical Inference and its Applications

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