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Asymptotic distributions of the latent roots of the covariance matrix with multiple population roots

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  • Chikuse, Yasuko

Abstract

An asymptotic expansion for large sample size n is derived by a partial differential equation method, up to and including the term of order n-2, for the 0F0 function with two argument matrices which arise in the joint density function of the latent roots of the covariance matrix, when some of the population latent roots are multiple. Then we derive asymptotic expansions for the joint and marginal distributions of the sample roots in the case of one multiple root.

Suggested Citation

  • Chikuse, Yasuko, 1976. "Asymptotic distributions of the latent roots of the covariance matrix with multiple population roots," Journal of Multivariate Analysis, Elsevier, vol. 6(2), pages 237-249, June.
  • Handle: RePEc:eee:jmvana:v:6:y:1976:i:2:p:237-249
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    Cited by:

    1. Peter D. Hoff, 2009. "A hierarchical eigenmodel for pooled covariance estimation," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(5), pages 971-992.

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