Timeline for Optimal hypothesis testing uses sufficient statistics?
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
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| Apr 25, 2023 at 9:34 | comment | added | Kweku A | There's more context I was trying to simplify from and I went too far, but your answer is already enough to help me think about it! I'm looking at a multiple testing setting, where we've managed to prove optimality of some tests (infimum over tests of supremum over a set of possible parameters of the false discovery rate plus false negative rate) in a location model, and I'm trying to work out minimal assumptions to do the same in a scale model. It's relatively clear what to do if you can limit attention to a sufficient statistic, but I'm not yet sure if that's allowed. Thanks for your help! | |
| Apr 25, 2023 at 9:33 | vote | accept | Kweku A | ||
| Apr 23, 2023 at 17:01 | comment | added | Iosif Pinelis | @KwekuA : In general, there is no uniformly most powerful test anyway. For instance, there is no uniformly most powerful test even in such a simple setting as testing $H_0\colon\theta=0$ vs. $H_1\colon\theta\ne0$ for an i.i.d. sample from $N(\theta,1)$. | |
| Apr 23, 2023 at 16:24 | comment | added | Kweku A | Thanks for a great response! I'm satisfied for the simple hypothesis case; in the composite case, Neyman--Pearson only gives optimality if the likelihood ratio test is uniformly most powerful, which in general isn't the case. | |
| Apr 23, 2023 at 16:04 | history | answered | Iosif Pinelis | CC BY-SA 4.0 |