Skip to main content
SpringerLink
Log in

A characterization of admissible linear estimators of fixed and random effects in linear models

  • Published:
Metrika Aims and scope Submit manuscript

Abstract

In the paper the problem of simultaneous linear estimation of fixed and random effects in the mixed linear model is considered. A necessary and sufficient conditions for a linear estimator of a linear function of fixed and random effects in balanced nested and crossed classification models to be admissible are given.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Azzam A-M, Birkes D, Seely J (1988) Admissibility in linear models with polyhedral covariance strukture. In: Graybill A, Srivastava JN (eds) Probability and statistics: essays in honor of Franklin, pp 1–8

  • Baksalary JK, Markiewicz A, Rao CR (1995) Admissiblelinear estimation in the general Gauss–Markov model with respect to an arbitrary quadratic risk function. J Stat Plann Inference 44:341–347

    Article  MATH  MathSciNet  Google Scholar 

  • Cohen A (1966) All admissible linear estimators of the mean vector. Ann Math Stat 37:458–463

    Article  MATH  Google Scholar 

  • Harville DA (1976) Extension of the Gauss-Markov theorem to include the estimation of random effects. Ann Stat 2:384–395

    Article  MathSciNet  Google Scholar 

  • Henderson CR (1973) Maximum likelihood estimation of variance components. Unpublished manuscript, Department of Animal Science, Cornell University, Ithaca

  • Klonecki W, Zontek S (1988) On the structure of admissible linear estimators. J Multivariate Anal 24:11–30

    Article  MATH  MathSciNet  Google Scholar 

  • LaMotte LR (1982) Admissibility in linear estimation. Ann Stat 10.1:245–255

    Article  MATH  MathSciNet  Google Scholar 

  • LaMotte LR (1997) On limits of uniquely best linear estimators. Metrika 45:197–211

    Article  MathSciNet  Google Scholar 

  • Mathew T, Rao CR, Sinha BK (1984) Admissible linear estimation in singular linear models. Commun Stat Theory Methods 13:3033–3045

    Article  MATH  MathSciNet  Google Scholar 

  • Rao CR (1976) Estimation of parameters in a linear model. Ann Stat 4:1023–1037

    Article  MATH  Google Scholar 

  • Rao CR (1987) Estimation in linear models with mixed effects: a unified theory. In: Proceedings of second international tampere conference in statistics. Department of Mathematical Sciences, University of Tampere, pp 73–98

  • Robinson GK (1991) That BLUP is a good thing-the estimation of random effects. Stat Sci 6:15–51

    Article  MATH  Google Scholar 

  • Shinozaki N (1975) A study of generalized inverse of matrix and estimation with quadratic loss. PhD Thesis, Keio University, Japan

  • Stȩpniak C (1987) A complete class for linear estimation in a general linear model. Ann Inst Stat Math 39:563–573

    Article  MathSciNet  Google Scholar 

  • Zontek S (1988) Admissibility of limits of the unique locally best linear estimators with application to variance components models. Prob Math Stat 9:29–44

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra, ul. prof. Z. Szafrana 4 a, 65-516, Zielona Góra, Poland

    Ewa Synówka-Bejenka & Stefan Zontek

Authors
  1. Ewa Synówka-Bejenka
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Stefan Zontek
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Stefan Zontek.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Synówka-Bejenka, E., Zontek, S. A characterization of admissible linear estimators of fixed and random effects in linear models. Metrika 68, 157–172 (2008). https://doi.org/10.1007/s00184-007-0149-0

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00184-007-0149-0

Keywords

Search

Navigation