IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v38y1998i4p347-354.html
   My bibliography  Save this article

Comparison of linear restricted models with respect to the validity of admissible and linearly sufficient estimators

Author

Listed:
  • Markiewicz, Augustyn

Abstract

Two restricted linear models M0 and M are considered. The models can differ in model matrices, dispersion matrices, and possibly in parameter restrictions. The validity under M of estimators that are admissible and linearly sufficient under M0 is studied. Criteria are derived for strong and week validity, i.e. when all estimators and at least one, respectively, preserve their properties. Some supplementary results for unrestricted model are also given.

Suggested Citation

  • Markiewicz, Augustyn, 1998. "Comparison of linear restricted models with respect to the validity of admissible and linearly sufficient estimators," Statistics & Probability Letters, Elsevier, vol. 38(4), pages 347-354, July.
  • Handle: RePEc:eee:stapro:v:38:y:1998:i:4:p:347-354
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(98)00045-5
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Baksalary, Jerzy K. & Mathew, Thomas, 1988. "Admissible linear estimation in a general Gauss-Markov model with an incorrectly specified dispersion matrix," Journal of Multivariate Analysis, Elsevier, vol. 27(1), pages 53-67, October.
    2. Mueller, Jochen, 1987. "Sufficiency and completeness in the linear model," Journal of Multivariate Analysis, Elsevier, vol. 21(2), pages 312-323, April.
    3. Rao, C. Radhakrishna, 1973. "Representations of best linear unbiased estimators in the Gauss-Markoff model with a singular dispersion matrix," Journal of Multivariate Analysis, Elsevier, vol. 3(3), pages 276-292, September.
    4. Markiewicz, Augustyn, 1996. "Characterization of general ridge estimators," Statistics & Probability Letters, Elsevier, vol. 27(2), pages 145-148, April.
    5. Heiligers, Berthold & Markiewicz, Augustyn, 1996. "Linear sufficiency and admissibility in restricted linear models," Statistics & Probability Letters, Elsevier, vol. 30(2), pages 105-111, October.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Liu, Xu-qing & Rong, Jian-ying, 2007. "Nonnegative quadratic estimation and quadratic sufficiency in general linear models," Journal of Multivariate Analysis, Elsevier, vol. 98(6), pages 1180-1194, July.
    2. Yongge Tian, 2017. "Transformation approaches of linear random-effects models," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 26(4), pages 583-608, November.
    3. Liu, Xu-Qing & Rong, Jian-Ying & Liu, Xiu-Ying, 2008. "Best linear unbiased prediction for linear combinations in general mixed linear models," Journal of Multivariate Analysis, Elsevier, vol. 99(8), pages 1503-1517, September.
    4. Liu, Xu-Qing & Wang, Dong-Dong & Rong, Jian-Ying, 2009. "Quadratic prediction and quadratic sufficiency in finite populations," Journal of Multivariate Analysis, Elsevier, vol. 100(9), pages 1979-1988, October.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Yongge Tian, 2017. "Transformation approaches of linear random-effects models," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 26(4), pages 583-608, November.
    2. Liu, Xu-qing & Rong, Jian-ying, 2007. "Nonnegative quadratic estimation and quadratic sufficiency in general linear models," Journal of Multivariate Analysis, Elsevier, vol. 98(6), pages 1180-1194, July.
    3. Liu, Xu-Qing & Wang, Dong-Dong & Rong, Jian-Ying, 2009. "Quadratic prediction and quadratic sufficiency in finite populations," Journal of Multivariate Analysis, Elsevier, vol. 100(9), pages 1979-1988, October.
    4. Ibarrola, P. & Pérez-Palomares, A., 2003. "Linear sufficiency and linear admissibility in a continuous time Gauss-Markov model," Journal of Multivariate Analysis, Elsevier, vol. 87(2), pages 315-327, November.
    5. Liu, Xu-Qing & Rong, Jian-Ying & Liu, Xiu-Ying, 2008. "Best linear unbiased prediction for linear combinations in general mixed linear models," Journal of Multivariate Analysis, Elsevier, vol. 99(8), pages 1503-1517, September.
    6. Ibarrola, P. & Pérez-Palomares, A., 2004. "Linear completeness in a continuous time Gauss-Markov model," Statistics & Probability Letters, Elsevier, vol. 69(2), pages 143-149, August.
    7. Haupt, Harry & Oberhofer, Walter, 2006. "Best affine unbiased representations of the fully restricted general Gauss-Markov model," Journal of Multivariate Analysis, Elsevier, vol. 97(3), pages 759-764, March.
    8. Guang Jing Song & Qing Wen Wang, 2014. "On the weighted least-squares, the ordinary least-squares and the best linear unbiased estimators under a restricted growth curve model," Statistical Papers, Springer, vol. 55(2), pages 375-392, May.
    9. Yongge Tian & Jieping Zhang, 2011. "Some equalities for estimations of partial coefficients under a general linear regression model," Statistical Papers, Springer, vol. 52(4), pages 911-920, November.
    10. Changli Lu & Yuqin Sun & Yongge Tian, 2013. "On relations between weighted least-squares estimators of parametric functions under a general partitioned linear model and its small models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 76(5), pages 707-722, July.
    11. Stepniak, C., 1997. "Sandwich theorem in comparison of multivariate normal experiments," Statistics & Probability Letters, Elsevier, vol. 33(3), pages 281-284, May.
    12. Lu, Changli & Gan, Shengjun & Tian, Yongge, 2015. "Some remarks on general linear model with new regressors," Statistics & Probability Letters, Elsevier, vol. 97(C), pages 16-24.
    13. Alan J. Rogers, 2013. "Concentration Ellipsoids, Their Planes of Support, and the Linear Regression Model," Econometric Reviews, Taylor & Francis Journals, vol. 32(2), pages 220-243, February.
    14. He, Daojiang & Wu, Jie, 2014. "Admissible linear estimators of multivariate regression coefficient with respect to an inequality constraint under matrix balanced loss function," Journal of Multivariate Analysis, Elsevier, vol. 129(C), pages 37-43.
    15. Jürgen Groß, 2004. "The general Gauss-Markov model with possibly singular dispersion matrix," Statistical Papers, Springer, vol. 45(3), pages 311-336, July.
    16. T. Caliński & S. Czajka & Z. Kaczmarek & P. Krajewski & W. Pilarczyk & I. Siatkowski & M. Siatkowski, 2017. "On a mixed model analysis of multi-environment variety trials: a reconsideration of the one-stage and the two-stage models and analyses," Statistical Papers, Springer, vol. 58(2), pages 433-465, June.
    17. Heiligers, Berthold & Markiewicz, Augustyn, 1996. "Linear sufficiency and admissibility in restricted linear models," Statistics & Probability Letters, Elsevier, vol. 30(2), pages 105-111, October.
    18. Tian, Yongge, 2009. "On an additive decomposition of the BLUE in a multiple-partitioned linear model," Journal of Multivariate Analysis, Elsevier, vol. 100(4), pages 767-776, April.
    19. Dong, Baomin & Guo, Wenxing & Tian, Yongge, 2014. "On relations between BLUEs under two transformed linear models," Journal of Multivariate Analysis, Elsevier, vol. 131(C), pages 279-292.
    20. Nesrin Güler & Melek Eriş Büyükkaya & Melike Yiğit, 2022. "Comparison of Covariance Matrices of Predictors in Seemingly Unrelated Regression Models," Indian Journal of Pure and Applied Mathematics, Springer, vol. 53(3), pages 801-809, September.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:stapro:v:38:y:1998:i:4:p:347-354. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.