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A Maximal Extension of the Gauss-Markov Theorem and Its Nonlinear Version

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  • Kariya, Takeaki
  • Kurata, Hiroshi

Abstract

In this paper, first we make a maximal extension of the well-known Gauss-Markov Theorem (GMT) in its linear framework. In particular, the maximal class of distributions of error term for which the GMT holds is derived. Second, we establish a nonlinear version of the maximal GMT and describe some interesting families of distributions of error term for which the nonlinear GMT holds.

Suggested Citation

  • Kariya, Takeaki & Kurata, Hiroshi, 2002. "A Maximal Extension of the Gauss-Markov Theorem and Its Nonlinear Version," Journal of Multivariate Analysis, Elsevier, vol. 83(1), pages 37-55, October.
    • Handle: RePEc:eee:jmvana:v:83:y:2002:i:1:p:37-55
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    References listed on IDEAS

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    1. Eaton, Morris L., 1986. "A characterization of spherical distributions," Journal of Multivariate Analysis, Elsevier, vol. 20(2), pages 272-276, December.
    2. Berk, Robert & Hwang, Jiunn T., 1989. "Optimality of the least squares estimator," Journal of Multivariate Analysis, Elsevier, vol. 30(2), pages 245-254, August.
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