Timeline for What is the mathematical characterization of sufficient statistics of a given $\sigma$-dominated probability model?
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| May 8, 2017 at 2:16 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
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| Dec 9, 2016 at 0:20 | comment | added | Henry.L | @RHahn I have made my attempt and it is a bit tangential to the paper you pointed out earlier. Thanks. | |
| Dec 9, 2016 at 0:13 | answer | added | Henry.L | timeline score: 2 | |
| Dec 4, 2016 at 5:31 | comment | added | Henry.L | @RHahn For example, what I am expecting is some relation like $\sigma(T)\subset\cap_{\theta}\sigma(P_{\theta})$. And possibly some equality holds when the $T$ is minimal sufficient for $\cal{P}$. Halmos-Savage paper led to "partition method" on spaces yet I do not know what "partition method" imply on associated $\sigma$-fields. | |
| Dec 4, 2016 at 4:51 | comment | added | R Hahn | I thought probably it didn't answer your question, but I wasn't sure exactly what you are asking, so I figured I would point to it. I'm not used to thinking about "$\sigma$-field generated by a dominated model". | |
| Dec 4, 2016 at 4:17 | comment | added | Henry.L | Actually the Neymann-Fisher factorization is also known as Halmos-Savage Theorem due to this paper. See [Casella&Berger,2002] for example. | |
| Dec 4, 2016 at 4:15 | comment | added | Henry.L | @RHahn It is a classical paper yet it does not address my problem. I am looking for more or less a relationship between $\sigma$-fields generated by sufficient statistics and those generated by a dominatd model $\cal{P}$. I came up with this question when I studied the gradient flows. I have actually made a few attempts looking into literature because such an inquiry seems naive at the first look. But thank you for your input. | |
| Dec 4, 2016 at 2:42 | comment | added | R Hahn | Does the paper by Halmos and Savage (1949) address your question? Theorem 1 in section 5 is phrased differently than Neyman-Fisher factorization, which is given as a corollary in section 6. projecteuclid.org/euclid.aoms/1177730032 | |
| Dec 4, 2016 at 0:56 | history | edited | Henry.L |
edit tag for possible better response
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| Dec 3, 2016 at 18:03 | history | edited | Henry.L | CC BY-SA 3.0 |
more precise title
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| Dec 3, 2016 at 17:49 | history | asked | Henry.L | CC BY-SA 3.0 |