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Inheriting independence and chi-squaredness under certain matrix orderings

Author

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  • Baksalary, Jerzy K.
  • Hauke, Jan

Abstract

Let x ~ N([mu], Z), and let S = ([Sigma]:[mu]). It is shown that if x'A1x is independent of x'Bx (x'A1x is distributed as a chi-square variable), then this property is inherited by every x'A2x for which S'A2S precedes S'A1S with respect to the range preordering (with respect to the rank subtractivity partial ordering).

Suggested Citation

  • Baksalary, Jerzy K. & Hauke, Jan, 1984. "Inheriting independence and chi-squaredness under certain matrix orderings," Statistics & Probability Letters, Elsevier, vol. 2(1), pages 35-38, January.
    • Handle: RePEc:eee:stapro:v:2:y:1984:i:1:p:35-38
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    Cited by:

    1. Mosić, Dijana & Djordjević, Dragan S., 2015. "Weighted pre-orders involving the generalized Drazin inverse," Applied Mathematics and Computation, Elsevier, vol. 270(C), pages 496-504.
    2. Hernández, A. & Lattanzi, M. & Thome, N., 2015. "Weighted binary relations involving the Drazin inverse," Applied Mathematics and Computation, Elsevier, vol. 253(C), pages 215-223.

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