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Chi-square mixture representations for the distribution of the scalar Schur complement in a noncentral Wishart matrix

Author

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  • Siriteanu, Constantin
  • Kuriki, Satoshi
  • Richards, Donald
  • Takemura, Akimichi

Abstract

We show that the distribution of the scalar Schur complement in a noncentral Wishart matrix is a mixture of central chi-square distributions with different degrees of freedom. For the case of a rank-1 noncentrality matrix, we reveal that the mixture weights arise from a noncentral beta mixture of Poisson distributions.

Suggested Citation

  • Siriteanu, Constantin & Kuriki, Satoshi & Richards, Donald & Takemura, Akimichi, 2016. "Chi-square mixture representations for the distribution of the scalar Schur complement in a noncentral Wishart matrix," Statistics & Probability Letters, Elsevier, vol. 115(C), pages 79-87.
    • Handle: RePEc:eee:stapro:v:115:y:2016:i:c:p:79-87
    DOI: 10.1016/j.spl.2016.02.016
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    Cited by:

    1. Elena Hadjicosta & Donald Richards, 2020. "Integral transform methods in goodness-of-fit testing, II: the Wishart distributions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(6), pages 1317-1370, December.

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