Timeline for Bounding $\|X_1/(X_1+X_2) - Y_1/(Y_1+Y_2)\|_p$ by the closeness of $X$ and $Y$
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
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| Oct 9, 2023 at 18:17 | comment | added | ArBo | How do you come up with these... Thanks! | |
| Oct 9, 2023 at 15:31 | comment | added | Iosif Pinelis | @ArBo : Such an additional condition does not help, alas. See the added response to your comments. | |
| Oct 9, 2023 at 15:30 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
added 602 characters in body
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| Oct 9, 2023 at 14:34 | comment | added | ArBo | I'll post a modified question in a few hours! I should definitely have mentioned this condition, but before seeing this counter-example, I didn't realise it was relevant (as it always goes, of course). I'll be careful to include all constraints in the modification. | |
| Oct 9, 2023 at 14:11 | comment | added | Iosif Pinelis | @ArBo : With this additional condition, I don't have an answer at the moment. So, I think it may be worth posting the modified question separately. In general, it may make sense to disclose at once all your cards that you would eventually disclose. | |
| Oct 9, 2023 at 9:49 | comment | added | ArBo | Again a clever counter-example! This gave me a lot of insight into the problem, so thanks for that. In my application, we have $X=\exp(-U)$ and $Y=\exp(-V)$ for random variables $U\ge0$ and $V\ge0$ of which all finite moments exist. In your example, $X_1 = \exp(-c/Z_1)$ with $Z_1$ uniformly random on $(0, 1)$, which means that it falls outside my application. Of course, you could not have known this :-) Do you think it is worth me repeating the question with this restriction, or will a bound still not exist in that setting? | |
| Oct 9, 2023 at 9:45 | vote | accept | ArBo | ||
| Oct 9, 2023 at 4:20 | history | answered | Iosif Pinelis | CC BY-SA 4.0 |