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Admissible linear estimators in the general Gauss–Markov model under generalized extended balanced loss function

Author

Listed:
  • Buatikan Mirezi

    (Çukurova University)

  • Selahattin Kaçıranlar

    (Çukurova University)

Abstract

This paper proposes a new generalized extended balanced loss function (GEBLF). Admissibility of linear estimators is characterized in the General Gauss–Markov model with respect to GEBLF. The sufficient and necessary conditions for linear estimators to be admissible with a dispersion matrix possibly singular among the set of linear estimators are obtained. It is stated that the results obtained under special conditions lead to the results known in the literature.

Suggested Citation

  • Buatikan Mirezi & Selahattin Kaçıranlar, 2023. "Admissible linear estimators in the general Gauss–Markov model under generalized extended balanced loss function," Statistical Papers, Springer, vol. 64(1), pages 73-92, February.
    • Handle: RePEc:spr:stpapr:v:64:y:2023:i:1:d:10.1007_s00362-022-01298-9
    DOI: 10.1007/s00362-022-01298-9
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    References listed on IDEAS

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    1. Stepniak, Czeslaw, 1989. "Admissible linear estimators in mixed linear models," Journal of Multivariate Analysis, Elsevier, vol. 31(1), pages 90-106, October.
    2. Markiewicz, Augustyn, 1996. "Characterization of general ridge estimators," Statistics & Probability Letters, Elsevier, vol. 27(2), pages 145-148, April.
    3. Cao, Ming-Xiang & He, Dao-Jiang, 2017. "Admissibility of linear estimators of the common mean parameter in general linear models under a balanced loss function," Journal of Multivariate Analysis, Elsevier, vol. 153(C), pages 246-254.
    4. Klonecki, W. & Zontek, S., 1988. "On the structure of admissible linear estimators," Journal of Multivariate Analysis, Elsevier, vol. 24(1), pages 11-30, January.
    5. Wan, Alan T. K., 1994. "Risk comparison of the inequality constrained least squares and other related estimators under balanced loss," Economics Letters, Elsevier, vol. 46(3), pages 203-210, November.
    6. Cao, Mingxiang, 2014. "Admissibility of linear estimators for the stochastic regression coefficient in a general Gauss–Markoff model under a balanced loss function," Journal of Multivariate Analysis, Elsevier, vol. 124(C), pages 25-30.
    7. Kazuhiro Ohtani & David Giles & Judith Giles, 1997. "The exact risk performance of a pre-test estimator in a heteroskedastic linear regression model under the balanced loss function," Econometric Reviews, Taylor & Francis Journals, vol. 16(1), pages 119-130.
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