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A new confidence interval for all characteristic roots of a covariance matrix

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Abstract

Confidence intervals for all of the characteristic roots of a sample covariance matrix are derived. Using a perturbation expansion, we obtain a new confidence interval for these roots. Then, we propose another confidence interval based on the results of Monte Carlo simulations. Since it is based on simulations, this new confidence interval is both narrower and more accurate than others when the difference between the largest and smallest characteristic roots of the population covariance matrix is large.

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References

  • Anderson GA (1965) An asymptotic expansion for the distribution of the latent roots of the estimated covariance matrix. Ann Math Stat 36:1153–1173

    Google Scholar 

  • Anderson TW (2003) An introduction to multivariate statistical analysis, 3rd edn. Wiley, New York

    MATH  Google Scholar 

  • James AT (1960) The distribution of the latent roots of the covariance matrix. Ann Math Stat 31:151–158

    Google Scholar 

  • Konishi S (1977) Asymptotic expansion for the distribution of a function of latent roots of the covariance matrix. Ann Inst Stat Math 29A:389–396

    Article  MATH  MathSciNet  Google Scholar 

  • Konishi S, Sugiyama T (1981) Improved approximations to distributions of the largest and the smallest latent roots of a Wishart matrix. Ann Inst Stat Math 33(1):27–33

    Article  MATH  MathSciNet  Google Scholar 

  • Krishnaiah PR (1978) Some recent developments on real multivariate distributions. Dev Stat 1: 135–169, Academic, New York

  • Shiotani M (1976) Recent development in asymptotic expansions for the nonnull distributions of the multivariate test statistics-II. Research paper No. 322, Department of Mathematic and Statistics, University of Calgary

  • Siotani M, Hayakawa T, Fujikoshi Y (1985) Modern multivariate statistical analysis: a graduate course and handbook. American Science Press, Columbus

    MATH  Google Scholar 

  • Sugiyama T (1970) Joint distribution of the extreme roots of a covariance matrix. Ann Math Stat 41:655–657

    MathSciNet  Google Scholar 

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Authors and Affiliations

  1. College of Sociology, Rikkyo University, 3-34-1 Nishi-Ikebukuro, Toshima-ku, Tokyo, 171-8501, Japan

    Fumitake Sakaori

  2. Department of Mathematics, Chuo University, 1-13-27 Kasuga, Bunkyo-ku, Tokyo, Japan

    Takayuki Yamada, Akihisa Kawamura & Takakazu Sugiyama

Authors
  1. Fumitake Sakaori
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  2. Takayuki Yamada
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  3. Akihisa Kawamura
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  4. Takakazu Sugiyama
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Correspondence to Fumitake Sakaori.

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Sakaori, F., Yamada, T., Kawamura, A. et al. A new confidence interval for all characteristic roots of a covariance matrix. Computational Statistics 22, 121–131 (2007). https://doi.org/10.1007/s00180-007-0028-1

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  • DOI: https://doi.org/10.1007/s00180-007-0028-1

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