Skip to main content
SpringerLink
Log in

The exact distribution of a criterion for testing the hypothesis that the covariance matrix is diagonal

  • Published:
Trabajos de estadistica y de investigacion operativa

Summary

This article gives the exact distribution, in the most general case, of the likelihood ratio criterion for testing the hypothesis that the component in ap-variate normal distribution are independetly distributed or equivalently, that the covariance matrix is diagonal. The exact distribution is given in Meijer’sG-function as well as in terms of simple computable functions. Some special cases are represented in terms of hypergeometric functions. The main techniques used are the techniques of inverse Mellin transforms, Calculus of residues and the properties of hypergeometric functions.

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

  1. ANDERSON, T.W. (1958).:An Introduction to Multivariate Statistical Analysis. Wiley, New York.

    MATH  Google Scholar 

  2. BOX, G.E.P. (1949).:A general distribution theory for a class of likelihood criteria. Biometrika. 36, 317–346.

    MathSciNet  Google Scholar 

  3. CONSUL, P.C. (1967).:On the exact distributions of the criterion W for testing sphericity in a p-variate normal distribution. Ann. Math. Statist. 38, 1170–1174.

    Article  MATH  MathSciNet  Google Scholar 

  4. ERDELYI, A. et AL. (1953).: HigherTranscendental Functions. Vol. I. McGraw-Hill, New York.

    Google Scholar 

  5. GIRSHICK, M.A. (1941).:The distribution of the ellipticity statistic L when the hypothesis is false. Terr. Magn. Atmos. Elect. 46, 455–457.

    Article  Google Scholar 

  6. LUKE, Y.L. (1969).:The Special Functions and Their Approximations. Vol. II. Academic Press, New York.

    MATH  Google Scholar 

  7. MAUCHLY, J.W. (1940).Significance test for sphericity of a normal n-variate distribution. Ann. Math. Statist. 11, 204–209.

    Article  MATH  MathSciNet  Google Scholar 

  8. MEIJER, C.S. (1946).:On the G-function. I–VIII. Proc. Kon. Neder. Acad. Van. Wet. 49, 227–237, 344–356, 457–469, 632–641, 765–772, 936–943, 1063–1072, 1165–1175.

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, McGill University, Montreal, Canada

    A. M. Mathai

Authors
  1. A. M. Mathai
    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

Mathai, A.M. The exact distribution of a criterion for testing the hypothesis that the covariance matrix is diagonal. Trab. Estad. Invest. Oper. 23, 111–124 (1972). https://doi.org/10.1007/BF03004952

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF03004952

Keywords

Search

Navigation