Skip to main content
Log in

The power of the likelihood ratio test for additional information in a multivariate linear model

  • Published:
Annals of the Institute of Statistical Mathematics Aims and scope Submit manuscript

Summary

This paper deals with the likelihood ratio test for additional information in a multivariate linear model. It is shown that the power of the likelihood ratio test procedure has a monotonicity property. Asymptotic approximations for the power are also obtained.

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. (1958).Introduction to Multivariate Statistical Analysis, Wiley, New York.

    MATH  Google Scholar 

  2. Anderson, T. W. (1963). Asymptotic theory for principal component analysis,Ann. Math. Statist.,34, 122–148.

    Article  MathSciNet  Google Scholar 

  3. Courant, R. and Hilbert, D. (1953).Methods of Mathematical Physics, 1, Interscience, New York.

    MATH  Google Scholar 

  4. Das Gupta, S., Anderson, T. W. and Mudholkar, G. (1964). Monotonicity of the power functions of some tests of the multivariate linear hypothesis,Ann. Math. Statist.,35, 200–205.

    Article  MathSciNet  Google Scholar 

  5. Fujikoshi, Y. (1973). Monotonicity of the power functions of some tests in general MANOVA models,Ann. Statist.,1, 388–391.

    Article  MathSciNet  Google Scholar 

  6. Fujikoshi, Y. (1974). Asymptotic expansions of the non-null distributions of three statistics in GMANOVA,Ann. Inst. Statist. Math.,26, 289–297.

    Article  MathSciNet  Google Scholar 

  7. McKay, R. J. (1977). Simultaneous procedures for variable selection in multiple discriminant analysis,Biometrika,64, 283–290.

    Article  MathSciNet  Google Scholar 

  8. Perlman, M. D. and Olkin, I. (1980). Unbiasedness of invariant test for MANOVA and other multivariate problems,Ann. Statist.,8, 1326–1341.

    Article  MathSciNet  Google Scholar 

  9. Rao, C. R. (1965).Linear Statistical Inference and Its Applications, Wiley, New York.

    MATH  Google Scholar 

  10. Rao, C. R. (1966). Covariance adjustment and related problems in multivariate analysis,Multivariate Analysis—I (ed. P. R. Krishnaiah), Academic Press, New York, 87–103.

    Google Scholar 

  11. Sugiura, N. and Fujikoshi, Y. (1969). Asymptotic expansions of the non-null distributions of the likelihood ratio criteria for multivariate linear hypothesis and independence,Ann. Math. Statist.,40, 942–952.

    Article  MathSciNet  Google Scholar 

  12. Sugiura, N. (1973). Further asymptotic formulas for the non-null distributions of three statistics for multivariate linear hypothesis,Ann. Inst. Statist. Math.,25, 153–163.

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

About this article

Cite this article

Fujikoshi, Y. The power of the likelihood ratio test for additional information in a multivariate linear model. Ann Inst Stat Math 33, 279–285 (1981). https://doi.org/10.1007/BF02480941

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02480941

AMS 1970 subject classifications

Key words and phrases

Navigation