Skip to main content
SpringerLink
Log in

Admissible linear estimators of the multivariate normal mean without extra information

  • Articles
  • Published:
Statistical Papers Aims and scope Submit manuscript

Abstract

Suppose y is normally distributed with mean IRn and covariance σ2V, where σ2>0 and V>0 is known. The n. s. conditions that a linear estimator Ay+a of μ be admissible in the class of all estimators of μ which depend only on y are derived. In particular, the usual estimator δ0(y)=y is admissible in this class. The results are applied to the normal linear model and the admissibilities of many well-known linear estimators are demonstrated.

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

  • Baksalary, J. K. and Markiewicz, A. (1988). Admissible Linear Estimators In The General Gauss-Markov Model. J. Statist. Plann. Inference, 19, 349–359.

    Article  MATH  MathSciNet  Google Scholar 

  • Berger, J. (1982). Admissible minimax estimation of a multivariate normal mean with arbitrary quadratic loss. Ann. Statist., 4, 223–226.

    Article  Google Scholar 

  • Cheng, Ping (1982). Admissibility of simulaneous estimation of several parameters. J. Sys. Sci. & Math. Scis., 2(3), 176–195.

    Google Scholar 

  • Cohen, A. (1966). All admissible linear estimates of the mean vector. Ann. Math. Statist., 37, 458–463.

    Article  MathSciNet  Google Scholar 

  • Hoerl, A. E. and Kennard, R. W. (1970). Ridge Regression: Biased estimation for nonorthogonal problems. Technometrics, 12, 55–67.

    Article  MATH  Google Scholar 

  • James, W. and Stein, C. (1961). Estimation with quadratic loss. Proc. Fouth Berkeley Symp. Math. Statist., Prob. 1 361–379.

    MathSciNet  Google Scholar 

  • Johnson, S. R. Reimer, S. C. and Rothrock, T. P. (1972). Principal Components and the Problem of multicollinarity. Metroeconomica, 25, 306–314.

    Article  MathSciNet  Google Scholar 

  • Judge, G. G. and Bock, M. E. (1978). The Statistical Implication of Pre-Test and Stein-Rule Estimators in Econometrics. North-Holland, Asterdam.

    Google Scholar 

  • Kendall, M. G. (1957). A course in multivariate analysis. Charles Griffin, London.

    Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  • LaMotte, L. R. (1982). Admissibility in linear estimation. Ann. Math. Statist., 10, 245–255.

    MATH  MathSciNet  Google Scholar 

  • Mathew, T., Rao, C. R. and Sinha, B. K. (1984). Admissible Linear Estimation In Singular Linear Models. Commun. Statist.-Theor. Meth., 13(24), 3033–3045.

    Article  MATH  MathSciNet  Google Scholar 

  • Mayer, L. S. and Willke, T. A. (1973). On biased estimation in linear models. Technometrics, 15, 495–508.

    Article  MathSciNet  Google Scholar 

  • Rao, C. R. (1976). Estimation of parameters in a linear model. Ann. Math. Statist., 4, 1023–1037.

    MATH  Google Scholar 

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

    Google Scholar 

  • Trenkler, G. (1978). An iteration estimator for a linear model. COMPSTAT 1978: Wien, 125–131, Physica-Verlag, Wien.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut für Statistik undOekonometrie, Universität Basel, Petersgraben 51, CH-4051, Basel, Switzerland

    L. Wang

Authors
  1. L. Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Wang, L. Admissible linear estimators of the multivariate normal mean without extra information. Statistical Papers 32, 155–165 (1991). https://doi.org/10.1007/BF02925488

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02925488

Key words

Search

Navigation