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Asymptotic distribution of the LR statistic for equality of the smallest eigenvalues in high-dimensional principal component analysis

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  • Fujikoshi, Yasunori
  • Yamada, Takayuki
  • Watanabe, Daisuke
  • Takakazu Sugiyama

Abstract

This paper deals with the distribution of the LR statistic for testing the hypothesis that the smallest eigenvalues of a covariance matrix are equal. We derive an asymptotic null distribution of the LR statistic when the dimension p and the sample size N approach infinity, while the ratio p/N converging on a finite nonzero limit c[set membership, variant](0,1). Numerical simulations revealed that our approximation is more accurate than the classical chi-square-type approximation as p increases in value.

Suggested Citation

  • Fujikoshi, Yasunori & Yamada, Takayuki & Watanabe, Daisuke & Takakazu Sugiyama, 2007. "Asymptotic distribution of the LR statistic for equality of the smallest eigenvalues in high-dimensional principal component analysis," Journal of Multivariate Analysis, Elsevier, vol. 98(10), pages 2002-2008, November.
    • Handle: RePEc:eee:jmvana:v:98:y:2007:i:10:p:2002-2008
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    1. Schott, James R., 2006. "A high-dimensional test for the equality of the smallest eigenvalues of a covariance matrix," Journal of Multivariate Analysis, Elsevier, vol. 97(4), pages 827-843, April.
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    Cited by:

    1. Kato, Naohiro & Yamada, Takayuki & Fujikoshi, Yasunori, 2010. "High-dimensional asymptotic expansion of LR statistic for testing intraclass correlation structure and its error bound," Journal of Multivariate Analysis, Elsevier, vol. 101(1), pages 101-112, January.

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