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Asymptotic Distributions and Confidence Intervals of Component Loading in Principal Component Analysis

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New Developments in Psychometrics

Summary

In principal component analysis, it is quite useful to know the values of a correlation coefficient between a principal component and an original variable. We seek for knowing a meaning of each principal component from their values. However, we do not know how reliable the value of the component loading is. For this purpose we investigate the distribution of the component loading. But it is difficult to obtain its exact distribution. Therefore, we derive an asymptotic expansion for the distribution of the component loading, and also construct the confidence intervals from the result.

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References

  1. Anderson, G.A. (1965). An asymptotic expansion for the distribution of the latent roots of the estimated covariance matrix. Ann. Math. Statist., 36, 1153 1173.

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  2. Anderson, T.W. (1963). Asymptotic theory for principal component analysis. Ann. Math. Statist., 34, 122–148.

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  3. Jolliffe, I.T. (1986). Principal Component Analysis, Springer-Verlag, New York.

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  4. Sugiura, N. (1976). Asymptotic expansions of the distributions of the latent roots and the latent vector of the Wishart and multivariate F matrices. J. Multi. Anal., 6, 500–525.

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  5. Sugiyama, T. (1983). An Introduction to Multivarate Data Analysis, Asakura Publishing, Tokyo. (in Japanese)

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Author information

Authors and Affiliations

  1. Department of Information and Culture, Niigata University of Information and International Studies, 3-1-1, Mizukino, Niigata-shi, Niigata, 950-2292, Japan

    Shin-ichi Tsukada

  2. Department of Mathematics, Chuo University, 1-13-27 Kasuga, Bunkyo-ku, Tokyo, 112-0003, Japan

    Takakazu Sugiyama

Authors
  1. Shin-ichi Tsukada
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  2. Takakazu Sugiyama
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Editor information

H. Yanai A. Okada K. Shigemasu Y. Kano J. J. Meulman

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© 2003 Springer Japan

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Tsukada, Si., Sugiyama, T. (2003). Asymptotic Distributions and Confidence Intervals of Component Loading in Principal Component Analysis. In: Yanai, H., Okada, A., Shigemasu, K., Kano, Y., Meulman, J.J. (eds) New Developments in Psychometrics. Springer, Tokyo. https://doi.org/10.1007/978-4-431-66996-8_79

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  • DOI: https://doi.org/10.1007/978-4-431-66996-8_79

  • Publisher Name: Springer, Tokyo

  • Print ISBN: 978-4-431-66998-2

  • Online ISBN: 978-4-431-66996-8

  • eBook Packages: Springer Book Archive

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