Skip to main content
SpringerLink
Log in

Risk performance of a pre-test estimator for normal variance with the Stein-variance estimator under the LINEX loss function

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

Abstract

In this paper, we derive the exact formula of the risk function of a pre-test estimator for normal variance with the Stein-variance (PTSV) estimator when the asymmetric LINEX loss function is used. Fixing the critical value of the pre-test to unity which is a suggested critical value in some sense, we examine numerically the risk performance of the PTSV estimator based on the risk function derived. Our numerical results show that although the PTSV estimator does not dominate the usual variance estimator when under-estimation is more severe than over-estimation, the PTSV estimator dominates the usual variance estimator when over-estimation is more severe. It is also shown that the dominance of the PTSV estimator over the original Stein-variance estimator is robust to the extension from the quadratic loss function to the LINEX loss function.

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

  • Abramowitz, M. and I.A. Stegun (Eds.) (1972),Handbook of Mathematical Functions, New York: Dover Publications.

    MATH  Google Scholar 

  • Giles, J.A. and D.E.A. Giles (1993), Preliminary-test estimation of the regression scale parameter when the loss function is asymmetricCommunications in Statistics-Theory and Methods, 22, 1709–1733.

    Article  MATH  MathSciNet  Google Scholar 

  • Ohtani, K. (1994), Risk behavior of a pre-test estimator for normal variance with the Stein-type estimator,Statistical Papers, 35, 163–168.

    Article  MATH  MathSciNet  Google Scholar 

  • Ohtani, K. (1995), Generalized ridge regression estimators under the LINEX loss function,Statistical Papers, 36, 99–110.

    Article  MATH  MathSciNet  Google Scholar 

  • Pandey, B.N. and G.C. Mishra (1991), Weighted estimators for a normal population variance,Communications in Statistics-Theory and Methods, 20, 235–247.

    Article  Google Scholar 

  • Press, W.H., S.A. Teukolsky, W.T. Vetterling and B.P. Flannery (1986),Numerical Recipes, New York: Cambridge University Press.

    Google Scholar 

  • Rai, O. (1996), A some times pool estimator of mean life under LINEX loss function,Communications in Statistics-Theory and Methods, 25, 2057–2067.

    Article  MATH  MathSciNet  Google Scholar 

  • Sadooghi-Alvandi, (1990), Estimation of the parameter of a Poisson distribution using a LINEX loss function,Australian Journal of Statistics, 32, 393–398.

    Article  MATH  MathSciNet  Google Scholar 

  • Srivastava, V.K. and B.B. Rao (1992), Estimation of disturbance variance in linear regression models under asymmetric loss function,Journal of Quantitative Economics, 8, 341–345.

    Google Scholar 

  • Stein, C. (1964), Inadmissibility of the usual estimator for the variance of a normal distribution with unknown mean,Annals of the Institute of Statistical Mathematics, 16, 155–160.

    Article  MathSciNet  Google Scholar 

  • Varian, H.R. (1975), A Bayesian approach to real estate assessment,Studies in Bayesian Econometrics and Statistics in Honor of Leonard J. Savage (S.E. Fienberg and A. Zellner (Eds.)), Amsterdam: North-Holland, 195–208.

    Google Scholar 

  • Zellner, A. (1986), Bayesian estimation and prediction using asymmetric loss functions,Journal of the American Statistical Association, 81, 446–451.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculty of Economics, Kobe University, Rokko, Nada-ku, 657, Kobe, Japan

    Kazuhiro Ohtani

Authors
  1. Kazuhiro Ohtani
    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

Ohtani, K. Risk performance of a pre-test estimator for normal variance with the Stein-variance estimator under the LINEX loss function. Statistical Papers 40, 75–87 (1999). https://doi.org/10.1007/BF02927111

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02927111

Keywords

Search

Navigation