Timeline for What is the mathematical characterization of sufficient statistics of a given $\sigma$-dominated probability model?
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| Jun 7, 2023 at 23:09 | comment | added | No-one | If I understand correctly, what you are saying is just that if $T$ is a sufficient statistic then, for all $t\in\mathbb{R}$ with $\mathbb{P}_\theta(T^{-1}(t))\neq 0$, $\mathbb{E}(X|T=t)=\frac{1}{\mathbb{P}_\theta(T^{-1}(t))}\int_{T^{-1}(t)}X d\mathbb{P}_\theta$ is independent of $\theta$. This is obviously true but I don't see how it can be considered a new characterisation of sufficient statistics in terms of their $\sigma$-algebras since it is exactly the usual definition. | |
| Dec 9, 2016 at 1:29 | history | edited | Henry.L | CC BY-SA 3.0 |
added 111 characters in body
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| Dec 9, 2016 at 0:27 | history | edited | Henry.L | CC BY-SA 3.0 |
major correction in notations.
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| Dec 9, 2016 at 0:21 | history | edited | Henry.L | CC BY-SA 3.0 |
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| Dec 9, 2016 at 0:13 | history | answered | Henry.L | CC BY-SA 3.0 |