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Covariance structure associated with an equality between two general ridge estimators

Author

Listed:
  • Koji Tsukuda

    (The University of Tokyo)

  • Hiroshi Kurata

    (The University of Tokyo)

Abstract

In the Gauss–Markov model, this paper derives a necessary and sufficient condition under which two general ridge estimators coincide with each other. The condition is given as a structure of the dispersion matrix of the error term. Since the class of estimators considered here contains linear unbiased estimators such as the ordinary least squares estimator and the best linear unbiased estimator, our result can be viewed as a generalization of the well known theorems on the equality between these two estimators, which have been fully studied in the literature. Two related problems are also considered: equality between two residual sums of squares, and classification of dispersion matrices by a perturbation approach.

Suggested Citation

  • Koji Tsukuda & Hiroshi Kurata, 2020. "Covariance structure associated with an equality between two general ridge estimators," Statistical Papers, Springer, vol. 61(3), pages 1069-1084, June.
    • Handle: RePEc:spr:stpapr:v:61:y:2020:i:3:d:10.1007_s00362-017-0975-8
    DOI: 10.1007/s00362-017-0975-8
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    References listed on IDEAS

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    1. Markiewicz, Augustyn, 1996. "Characterization of general ridge estimators," Statistics & Probability Letters, Elsevier, vol. 27(2), pages 145-148, April.
    2. Oskar Baksalary & Götz Trenkler, 2009. "A projector oriented approach to the best linear unbiased estimator," Statistical Papers, Springer, vol. 50(4), pages 721-733, August.
    Full references (including those not matched with items on IDEAS)

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