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- W4301474876 abstract "If the space $mathcal{Q}$ of quadratic forms in $mathbb{R}^n$ is splitted in a direct sum $mathcal{Q}_1oplus...oplus mathcal{Q}_k$ and if $X$ and $Y$ are independent random variables of $mathbb{R}^n$, assume that there exist a real number $a$ such that $E(X|X+Y)=a(X+Y)$ and real distinct numbers $b_1,...,b_k$ such that $E(q(X)|X+Y)=b_iq(X+Y)$ for any $q$ in $mathcal{Q}_i.$ We prove that this happens only when $k=2$, when $mathbb{R}^n$ can be structured in a Euclidean Jordan algebra and when $X$ and $Y$ have Wishart distributions corresponding to this structure." @default.
- W4301474876 created "2022-10-05" @default.
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- W4301474876 date "2010-04-19" @default.
- W4301474876 modified "2023-09-26" @default.
- W4301474876 title "Why Jordan algebras are natural in statistics:quadratic regression implies Wishart distributions" @default.
- W4301474876 doi "https://doi.org/10.48550/arxiv.1004.3148" @default.
- W4301474876 hasPublicationYear "2010" @default.
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