Inheriting independence and chi-squaredness under certain matrix orderings

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).

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Year of publication:	1984
Authors:	Baksalary, Jerzy K. ; Hauke, Jan
Published in:	Statistics & Probability Letters. - Elsevier, ISSN 0167-7152. - Vol. 2.1984, 1, p. 35-38
Publisher:	Elsevier
Keywords:	quadratic form independence chi-squaredness range preordering Löwner partial ordering rank subtractivity partial ordering

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Type of publication:	Article
Source:	RePEc - Research Papers in Economics

Persistent link: https://www.econbiz.de/10005211860