Khatri, C. G. ; Radhakrishna Rao, C.
(1981)
*Some extensions of the Kantorovich inequality and statistical applications*
Journal of Multivariate Analysis, 11
(4).
pp. 498-505.
ISSN 0047-259X

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Official URL: http://linkinghub.elsevier.com/retrieve/pii/004725...

Related URL: http://dx.doi.org/10.1016/0047-259X(81)90092-0

## Abstract

Kantorovich gave an upper bound to the product of two quadratic forms, (X'AX) (X'A^{-1}X), where
X is an n-vector of unit length and A is a positive definite matrix. Bloomfield, Watson and Knott found the bound
for the product of determinants |X'AX| |X'A^{-1}X| where X is n × k matrix such that X'X =
I_{k}. In this paper we determine the bounds for the traces and determinants of matrices of the type
X'AYY'A^{-1}X, X'B^{2}X(X'BCX)^{-1} X'C^{2}X(X'BCX)^{-1} where X and Y are
n × k matrices such that X'X = Y'Y = I_{k} and A, B, C are given matrices satisfying some conditions.
The results are applied to the least squares theory of estimation.

Item Type: | Article |
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Source: | Copyright of this article belongs to Elsevier Science. |

Keywords: | Kantorovich Inequality; Inverse Cauchy Inequality; least Squares; Efficiency; Regression |

ID Code: | 42489 |

Deposited On: | 04 Jun 2011 09:09 |

Last Modified: | 04 Jun 2011 09:09 |

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