Skip to main content
Log in

On the jackknife statistics for eigenvalues and eigenvectors of a correlation matrix

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

Abstract

This paper deals with some problems of eigenvalues and eigenvectors of a sample correlation matrix and derives the limiting distributions of their jackknife statistics with some numerical examples.

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.

Similar content being viewed by others

References

  • Bellman R. (1960). Introduction to Matrix Analysis, McGraw-Hill, New York.

    MATH  Google Scholar 

  • Beran R. (1984). Jackknife approximations to bootstrap estimates, Ann. Statist., 12, 101–118.

    Article  MathSciNet  Google Scholar 

  • Beran R. and Srivastava M. S. (1985). Bootstrap tests and confidence regions for functions of a covariance matrix, Ann. Statist., 13, 95–115.

    Article  MathSciNet  Google Scholar 

  • Fang C. and Krishnaiah P. R. (1982). Asymptotic distributions of functions of the eigenvalues of some random matrices for nonnormal populations, J. Multivariate Anal., 12, 39–63.

    Article  MathSciNet  Google Scholar 

  • Goto M. and Tazaki T. (1978). Methods of jackknife inference, Quality and Control., 8, 120–129 (in Japanese).

    Google Scholar 

  • Hinkley D. V. (1978). Improving the jackknife with special reference to correlation estimation, Biometrika, 65, 13–21.

    Article  MathSciNet  Google Scholar 

  • Konishi S. (1979). Asymptotic expansions for the distributions of statistics based on the sample correlation matrix in principal component analysis, Hiroshima Math. J., 9, 647–700.

    MathSciNet  MATH  Google Scholar 

  • Lawley D. N. (1963). On testing a set of correlation coefficients for equality, Ann. Math. Statist., 34, 149–151.

    Article  MathSciNet  Google Scholar 

  • Miller R. G.Jr. (1974). The jackknife: a review, Biometrika, 61, 1–15.

    MathSciNet  MATH  Google Scholar 

  • Nagao H. (1985). On the limiting distributions of the jackknife statistics for eigenvalues of a sample covariance matrix, Comm. Statist. A—Theory Methods, 14, 1547–1567.

    Article  MathSciNet  Google Scholar 

  • Parr W. C. and Schucany W. R. (1980). The jackknife: a bibliography, Internat. Statist. Rev., 48, 73–78.

    MathSciNet  MATH  Google Scholar 

  • Rao C. R. (1964). The use and interpretation of principal component analysis in applied research, Sankhyā Ser. A, 26, 329–358.

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

About this article

Cite this article

Nagao, H. On the jackknife statistics for eigenvalues and eigenvectors of a correlation matrix. Ann Inst Stat Math 40, 477–489 (1988). https://doi.org/10.1007/BF00053060

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00053060

Key words and phrases

Navigation