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Kantorovich-type inequalities and the measures of inefficiency of the glse

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Abstract

In this paper we introduce some Kantorovich inequalities for the Euclidean norm of a matrix, that is, the upper bounds to ∥(X'B −1 X) −1 X'B −1 AB −1 X(X'B −1X)−1 X' BX(X'AX) −1 X'CX∥2 are given, where ∥A∥2=trace (A'A). In terms of these inequalities the upper bounds to the three measures of inefficiency of the generalized least squares estimator (GLSE) in general Gauss-Markov models are also established.

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Authors and Affiliations

  1. University of Science and Technology of China, China

    Wang Songgui

  2. Chongqing Communication Institute, China

    Yang Hu

Authors
  1. Wang Songgui
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  2. Yang Hu
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Additional information

Project supported partially by the Third World Academy of Sciences under contract TWASRG 87-46 and by the National Natural Science Foundation.

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Wang, S., Yang, H. Kantorovich-type inequalities and the measures of inefficiency of the glse. Acta Mathematicae Applicatae Sinica 5, 372–381 (1989). https://doi.org/10.1007/BF02005959

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  • DOI: https://doi.org/10.1007/BF02005959

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