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Some extensions of the Kantorovich inequality and statistical applications. (English) Zbl 0482.15010

15A42Inequalities involving eigenvalues and eigenvectors
15A63Quadratic and bilinear forms, inner products
15A15Determinants, permanents, other special matrix functions
62J05Linear regression
15A18Eigenvalues, singular values, and eigenvectors
Full Text: DOI
[1] Bloomfield, P.; Watson, G. S.: The inefficiency of least squares. Biometrika 62, 121-128 (1975) · Zbl 0308.62056
[2] Greub, W.; Rheinboldt, W.: On a generalization of an inequality of L. V. Kantorovich. Proc. amer. Math. soc. 10, 407-415 (1959) · Zbl 0093.12405
[3] Knott, M.: On the minimum efficiency of least squares. Biometrika 62, 129-132 (1975) · Zbl 0308.62057
[4] Rao, C. Radhakrishna: Least squares theory using an estimated dispersion mtrix and its application to measurement of signals. Proc. fifth. Berkeley symp., 355-373 (1967)
[5] Rao, C. Radhakrishna: 2nd ed. Linear statistical inference and its applications. Linear statistical inference and its applications (1973) · Zbl 0256.62002
[6] Rao, C. Radhakrishna: Separation theorems for singular values of matrices and their applications in multivariate analysis. J. multivar. Analysis 9, 362-377 (1979) · Zbl 0445.62069
[7] Strang, W. G.: On the Kantorovich inequality. Proc. amer. Math. soc. 11, 468 (1960) · Zbl 0095.09601