The Lukacs–Olkin–Rubin Theorem on Symmetric Cones Without Invariance of the “Quotient”

Bartosz Kołodziejek ()
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Bartosz Kołodziejek: Warsaw University of Technology

Journal of Theoretical Probability, 2016, vol. 29, issue 2, 550-568

Abstract: Abstract We prove the Lukacs–Olkin–Rubin theorem without invariance of the distribution of the “quotient,” which was the key assumption in the original proof of (Olkin–Rubin in Ann Math Stat 33:1272–1280, 1962). Instead, we assume existence of strictly positive continuous densities of respective random variables. We consider the (cone variate) “quotient” for any division algorithm satisfying some natural conditions. For that purpose, a new proof of the Olkin–Baker functional equation on symmetric cones is given.

Keywords: Lukacs characterization; Division algorithm; Wishart distribution; Riesz distribution; Symmetric cones; Functional equations; 62H05 (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s10959-014-0587-3

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