Why Jordan algebras are natural in statistics: quadratic regression implies Wishart distributions
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چکیده
منابع مشابه
Why Jordan Algebras Are Natural in Statistics: Quadratic Regression Implies Wishart Distributions
— If the space Q of quadratic forms in Rn is splitted in a direct sum Q1 ⊕ · · · ⊕ Qk and if X and Y are independent random variables of Rn, assume that there exist a real number a such that E(X|X + Y ) = a(X + Y ) and real distinct numbers b1, ..., bk such that E(q(X)|X + Y ) = biq(X + Y ) for any q in Qi. We prove that this happens only when k = 2, when Rn can be structured in a Euclidean Jor...
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ژورنال
عنوان ژورنال: Bulletin de la Société mathématique de France
سال: 2011
ISSN: 0037-9484,2102-622X
DOI: 10.24033/bsmf.2603