An Iterated Version on the Gauss-Markov Theorem in Generalized Least Squares Estimation

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タイトル別名
  • AN ITERATED VERSION OF THE GAUSS-MARKOV THEOREM IN GENERALIZED LEAST SQUARES ESTIMATION
  • Iterated Version on the Gauss Markov Th

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In the general linear model with covariance structure, depending on an unknown parameter vector, it is shown that the greatest lower bound for the risk matrix of the generalized least squares estimator (GLSE) constructed with covariance structure estimated from the iterated residuals is that of the Gauss-Markov estimator. A sufficient condition for the existence and the unbiasedness of the GLSE based on iterated residuals is given. It is shown that the use of the iterated residuals does not improve the risk matrix of GLSE through terms of order n-2 relative to that of the two step estimator.

収録刊行物

  • 日本統計学会誌

    日本統計学会誌 17 (2), 129-136, 1987

    一般社団法人 日本統計学会

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