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On the ratios of the individual latent roots to the trace of a Wishart matrix

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  • Davis, A. W.

Abstract

A simple relationship is given between the exact null distribution gm,n(J) of the J-th largest latent root of an m - m Wishart matrix on n degrees of freedom, and the distribution fm,n(J) of the ratio of this root to the trace of the matrix. Explicit expressions for certain fm,n(J) may thus be obtained from previous results for the corresponding gm,n(J).

Suggested Citation

  • Davis, A. W., 1972. "On the ratios of the individual latent roots to the trace of a Wishart matrix," Journal of Multivariate Analysis, Elsevier, vol. 2(4), pages 440-443, December.
    • Handle: RePEc:eee:jmvana:v:2:y:1972:i:4:p:440-443
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    Cited by:

    1. Ferre, Louis, 1995. "Selection of components in principal component analysis: A comparison of methods," Computational Statistics & Data Analysis, Elsevier, vol. 19(6), pages 669-682, June.
    2. Nadler, Boaz, 2011. "On the distribution of the ratio of the largest eigenvalue to the trace of a Wishart matrix," Journal of Multivariate Analysis, Elsevier, vol. 102(2), pages 363-371, February.
    3. He, Yinqiu & Xu, Gongjun, 2018. "Estimating tail probabilities of the ratio of the largest eigenvalue to the trace of a Wishart matrix," Journal of Multivariate Analysis, Elsevier, vol. 166(C), pages 320-334.

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