Skip to main content
Log in

Some optima of parameter tests for elliptically contoured distribution class

  • Published:
Acta Mathematicae Applicatae Sinica Aims and scope Submit manuscript

Abstract

This paper proves that for elliptically contoured distributions many likelihood ratio tests are uniformly most powerful or unbiased.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Anderson, T. W., The intergral of a symmetric unimodal function over a symmetric convex set and some probability inequalities,Proc. Amer. Math. Soc.,6 (1955), 170–176.

    Google Scholar 

  2. Anderson, T. W. and Fang, K. T., Maximum likelihood estimators and likelihood ratio criteria for Multivariate elliptically contoured distributions. Technical Report of Statistics, Stanford University, 1982.

  3. Brown, G. W., On the power of theL 1 test for equality of several variance,Ann. Math. Statist.,10 (1939), 119–128.

    Google Scholar 

  4. Das, Gupta. S., Properties of power function of some tests concerning dispersion matrices of multivariate normal distribution,Ann. Math. Statist.,40 (1969), 697–701.

    Google Scholar 

  5. Giri, N. C., Multivariate Statistical Inference. Academic Press, New York, 1977.

    Google Scholar 

  6. Kariya, T. and Eaton, M. L., Robust test for spherical symmetry,Ann. Stat.,5 (1977), 206–215.

    Google Scholar 

  7. Muirhead, Robb. J., Aspects of Multivariate Statistical Theory. John Wiley and Sons, Inc., 1982.

  8. Perlman, M. D., Unbiasedness of the likelihood ratio test for equality of several covariance matrices and equality of several multivariate normal population,Ann. Stat.,8 (1980), 247–263.

    Google Scholar 

  9. Srivastara, M. S. and Khatric, C. G., An Introduction to Multivariate Statistics. North Holland, New York, 1979.

    Google Scholar 

  10. Fang Kaitai, A review of generalized multivariate analysis—Theory of elliptically contoured distribution class theory,Advances in Mathematics (to appear).

  11. Fan Jianqin, Generalized non-centralt, F, T 2 distribution,J. of Graduate School,2 (1985), 134–148.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Quan, H. Some optima of parameter tests for elliptically contoured distribution class. Acta Mathematicae Applicatae Sinica 3, 1–14 (1987). https://doi.org/10.1007/BF02112640

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02112640

Keywords

Navigation