Inheriting independence and chi-squaredness under certain matrix orderings

Jerzy K. Baksalary and Jan Hauke ()

Statistics & Probability Letters, 1984, vol. 2, issue 1, 35-38

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).

Keywords: quadratic; form; independence; chi-squaredness; range; preordering; Löwner; partial; ordering; rank; subtractivity; partial; ordering (search for similar items in EconPapers)
Date: 1984
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Citations: View citations in EconPapers (2)

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