The Lukacs–Olkin–Rubin Theorem on Symmetric Cones Without Invariance of the “Quotient”
The Lukacs–Olkin–Rubin Theorem on Symmetric Cones Without Invariance of the “Quotient”
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, Ann. Math. Stat. 33 (1962), 1272--1280]. Instead we assume existence of strictly positive continuous densities of respective random variables. We consider the (cone variate) "quotient" for …