Skip to main content
SpringerLink
Log in

An asymptotic expansion for the distribution of the determinant of a multivariate quadratic form in a normal sample

  • 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

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

References

  1. Constantine, A. G. (1963). Some non-central distribution problems in multivariate analysis,Ann. Math. Statist.,34, 1270–1285.

    MATH  MathSciNet  Google Scholar 

  2. Fujikoshi, Y. (1968). Asymptotic expansion of the distribution of the generalized variance in the non-central case,J. Sci. Hiroshima Univ., Ser. A-I,32, 293–299.

    MATH  MathSciNet  Google Scholar 

  3. Fujikoshi, Y. (1970). Asymptotic expansions of the distributions of test statistics in multivariate analysis,J. Sci. Hiroshima Univ., Ser. A-I,34, 73–144.

    MATH  MathSciNet  Google Scholar 

  4. Hayakawa, T. (1966). On the distribution of a quadratic form in multivariate normal sample,Ann. Inst. Statist. Math.,18, 191–201.

    Article  MATH  MathSciNet  Google Scholar 

  5. Hayakawa, T. (1969). On the distribution of the latent roots of a positive definite random symmetric matrix I,Ann. Inst. Statist. Math.,21, 1–21.

    MATH  MathSciNet  Google Scholar 

  6. Hayakawa, T. (1972). On the distribution of the multivariate quadratic form in multivariate normal samples,Ann. Inst. Math. Statist.,24, 205–230.

    MATH  MathSciNet  Google Scholar 

  7. Hayakawa, T. (1972). Note on the asymptotic distributions of the functions of an multivariate quadratic form in normal sample,Ann. Inst. Statist. Math.,24, 509–515.

    MATH  MathSciNet  Google Scholar 

  8. Hayakawa, T. (1972). The asymptotic distributions of the statistics based on the complex Gaussian distribution,Ann. Inst. Statist. Math.,24, 231–244.

    MATH  MathSciNet  Google Scholar 

  9. Hayakawa, T. (1972). On the asymptotic distribution of the determinant of the multivariate quadratic form in normal sample,Research Memorandum, No. 47., Inst. of Statist. Math., Tokyo.

    Google Scholar 

  10. Hayakawa, T. (1972). Further contribution to the asymptotic distribution of the determinant of the multivariate quadratic form in normal sample,Research Memorandum, No. 48, Inst. Statist. Math., Tokyo.

    Google Scholar 

  11. Hill, G. W. and Davis, A. W. (1968). Generalized asymptotic expansions of Cornish-Fisher type,Ann. Math. Statist.,39, 1264–1273.

    MATH  MathSciNet  Google Scholar 

  12. 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 

  13. Khatri, C. G. (1966). On certain distribution problems based on positive definite quadratic functions in normal vectors,Ann. Math. Statist.,37, 468–479.

    MATH  MathSciNet  Google Scholar 

  14. Shah, B. H. (1970). Distribution theory of positive definite quadratic form with matrix argument,Ann. Math. Statist.,41, 692–697.

    MATH  MathSciNet  Google Scholar 

  15. 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.

    MATH  MathSciNet  Google Scholar 

Download references

Authors
  1. Takesi Hayakawa
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

This work was begun in Department of Mathematics in Indiana University, U.S.A., and was supported by NSF Grant No. GP27715, and was completed at the Institute of Statistical Mathematics.

The Institute of Statistical Mathematics

About this article

Cite this article

Hayakawa, T. An asymptotic expansion for the distribution of the determinant of a multivariate quadratic form in a normal sample. Ann Inst Stat Math 25, 395–406 (1973). https://doi.org/10.1007/BF02479385

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02479385

Keywords

Search

Navigation