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Approximations for the distributions of the extreme latent roots of three matrices

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Summary

In this paper we present simple approximations for the distributions of the extreme latent roots of three matrices occurring in multivariate analysis. The matrices considered are (i)S 1 S 2 −1 whereS 1 andS 2 are independent Wishart matrices estimating different covarance matrices, (ii)S 1 S 2 −1 whereS 1 andS 2 are independent and estimate the same covariance matrix, withS 2 having the Wishart distribution andS 1 having the noncentral Wishart distribution, and (iii) the noncentral Wishart matrix. The approximations take the form of upper and lower bounds for the distribution functions of the largest and smallest latent roots respectively. For the three matrices considered above these bounds are expressed very simply in terms of products of (i)F, (ii) noncentralF and (iii) noncentralX 2 probabilities.

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Authors and Affiliations

  1. Yale University, New Haven, USA

    Robb J. Muirhead & Yasuko Chikuse

  2. Radiation Effects Research Foundation, Japan

    Robb J. Muirhead & Yasuko Chikuse

Authors
  1. Robb J. Muirhead
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  2. Yasuko Chikuse
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Muirhead, R.J., Chikuse, Y. Approximations for the distributions of the extreme latent roots of three matrices. Ann Inst Stat Math 27, 473–478 (1975). https://doi.org/10.1007/BF02504664

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  • DOI: https://doi.org/10.1007/BF02504664

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