Skip to main content

Asymptotic Distributions of Functions of Eigenvalues

  • Conference paper
  • 453 Accesses

Part of the book series: NATO Advanced Study Institutes Series ((ASIC,volume 79))

Summary

A brief review of some recent developments of asymptotic distributions of eigenvalues is given. Emphasis is on the joint distributions of analytic functions of eigenvalues. The random matrices considered are Wishart, correlation, MANOVA, and canonical correlation.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Anderson, T. W. (1951). The asymptotic distribution of certain characteristic roots and vectors. Proceedings 2nd Berkeley Symposium on Mathematical Statistics and Probability, J. Neyman, ed. University of California Press. Pages 103–130.

    Google Scholar 

  • Appel, P. and Kampe De Feriet, J. (1926). Functions Hyper-geometriques et Hypersperiques. Gauthier-Villar, Paris.

    Google Scholar 

  • Fujikoshi, Y. (1978). Asymptotic expansions for the distri-bution of some functions of the latent roots of matrices in three situations. Journal of Multivariate Analysis, 8, 63–72.

    Article  MathSciNet  MATH  Google Scholar 

  • Konishi, S. (1978). Asymptotic expansions for the distributions of statistics based on a correlation matrix. Canadian Journal of Statistics, 6, 49–56.

    Article  MathSciNet  MATH  Google Scholar 

  • Krishnaiah, P. R. and Lee, J. C. (1977). Inference on the eigenvalue of the covariance matrices of real and complex multivariate normal populations. In Multivariate Analysis IV, P. R. Krishnaiah, ed. North-Holland Publishing Company. Pages 95–103.

    Google Scholar 

  • Krishnaiah, P. R. and Lee, J. C. (1979). On the asymptotic joint distributions of certain functions of the eigenvalues of four random matrices. Journal of Multivariate Analysis, 9, 248–258.

    Article  MathSciNet  MATH  Google Scholar 

  • Lawley, D. N. (1956). Tests of significance for the latent roots of covariance and correlation matrices. Biometrika, 43, 128–136.

    Google Scholar 

  • Lee, J. C. and Krishnaiah, P. R. (1980). On the asymptotic distributions of certain functions of eigenvalues of correl-ation matrices. Banach Center Publications, 6, 229–237.

    MathSciNet  Google Scholar 

  • Sugiyama, T. and Tong, H. (1976). On a statistic useful in dimensionality reduction in multivariate linear stochastic system. Communications in Statistics–Theory and Methods, A5, 711–721.

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1981 D. Reidel Publishing Company

About this paper

Cite this paper

Lee, J.C. (1981). Asymptotic Distributions of Functions of Eigenvalues. In: Taillie, C., Patil, G.P., Baldessari, B.A. (eds) Statistical Distributions in Scientific Work. NATO Advanced Study Institutes Series, vol 79. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-8549-0_25

Download citation

  • DOI: https://doi.org/10.1007/978-94-009-8549-0_25

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-009-8551-3

  • Online ISBN: 978-94-009-8549-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics