Skip to main content
Log in

On an asymptotic distribution of the characteristic roots ofS 1 S 2 −1 when roots are not all distinct

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

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.

References

  1. Anderson, G. A. (1965). An asymptotic expansion for the distribution of the latent root of the estimated covariance matrix,Ann. Math. Statist.,36, 1153–1173.

    MATH  MathSciNet  Google Scholar 

  2. Anderson, T. W. (1948). The asymptotic distribution of the roots of certain determinantal equations,Roy. Stat. Soc.,10, 132–139.

    MATH  Google Scholar 

  3. Chang, T. C. (1970). On an asymptotic representation of the distribution of the characteristic roots ofS 1 S 2 −1,Ann. Math. Statist.,41, 440–445.

    MATH  MathSciNet  Google Scholar 

  4. Erdelyi, A. (1965).Asymptotic Expansions, Dover, New York.

    MATH  Google Scholar 

  5. Hsu, L. C. (1948). A theorem on the asymptotic behavior of a multiple integral,Duke Math. J.,15, 623–632.

    Article  MATH  MathSciNet  Google Scholar 

  6. Li, Hung C., Pillai, K. C. S. and Chang, Tseng C. (1970). Asymptotic expansions for distribution of the roots of two matrices from classical and complex Gaussian populations,Ann. Math. Statist.,41, 1541–1556.

    MATH  MathSciNet  Google Scholar 

  7. James, A. T. (1954). Normal multivariate analysis and the orthogonal group,Ann. Math. Statist.,25, 40–75.

    MATH  Google Scholar 

  8. James, A. T. (1960). The distribution of the latent roots of the covariance matrix,Ann. Math. Statist.,31, 151–158.

    MATH  MathSciNet  Google Scholar 

  9. James, A. T. (1964). Distributions of matrix variates and latent roots derived from normal samples,Ann. Math. Statist.,35, 475–501.

    MATH  MathSciNet  Google Scholar 

  10. James, A. T. (1969). Tests of equality of latent roots of the covariance matrix,Multivariate Analysis,2, (P. R. Krishnaiah, Ed.) Academic Press, New York.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

This research was supported by the National Science Foundation Grant No. GP-7663.

About this article

Cite this article

Chang, T.C. On an asymptotic distribution of the characteristic roots ofS 1 S 2 −1 when roots are not all distinct. Ann Inst Stat Math 25, 447–451 (1973). https://doi.org/10.1007/BF02479389

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02479389

Keywords

Navigation