Skip to main content
Log in

Note on the asymptotic distributions of the functions of a multivariate quadratic form in 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

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., 1270–1285.

  2. 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 

  3. 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 

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

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

    MATH  MathSciNet  Google Scholar 

  6. 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 

  7. 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 

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

    MATH  MathSciNet  Google Scholar 

Download references

Authors

Additional information

This work was partly supported by National Science Foundation under Grant No. GP. 27715.

About this article

Cite this article

Hayakawa, T. Note on the asymptotic distributions of the functions of a multivariate quadratic form in normal sample. Ann Inst Stat Math 24, 509–515 (1972). https://doi.org/10.1007/BF02479779

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02479779

Keywords

Navigation