Timeline for Concentration of sum of concentrated random variables
Current License: CC BY-SA 4.0
25 events
| when toggle format | what | by | license | comment | |
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| Apr 30, 2020 at 6:21 | answer | added | user2316602 | timeline score: 0 | |
| Jan 30, 2020 at 16:50 | vote | accept | user2316602 | ||
| Jan 30, 2020 at 16:43 | answer | added | fedja | timeline score: 6 | |
| Jan 30, 2020 at 12:56 | comment | added | user2316602 | Yes, I have updated the question | |
| Jan 30, 2020 at 12:56 | history | edited | user2316602 | CC BY-SA 4.0 |
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| Jan 30, 2020 at 12:52 | comment | added | fedja | Are $X_i$ posiitve? | |
| Jan 30, 2020 at 10:13 | comment | added | user2316602 | Let us continue this discussion in chat. | |
| Jan 30, 2020 at 9:34 | comment | added | user44143 | This still qualifies as “needs details or clarity”, so I’ll stop commenting. | |
| Jan 30, 2020 at 9:30 | comment | added | user2316602 | I have done so, as well as removing a part that was wrong. | |
| Jan 30, 2020 at 9:29 | history | edited | user2316602 | CC BY-SA 4.0 |
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| Jan 30, 2020 at 9:25 | comment | added | user44143 | The central proposition is still in the middle of a complicated sentence. It would help to isolate and state that proposition in a self-contained paragraph. Then the comments about what to expect can go in a different paragraph. It would also help to clarify which of the four questions indicated with question marks is the key question. | |
| Jan 30, 2020 at 9:25 | review | Close votes | |||
| Feb 7, 2020 at 3:00 | |||||
| Jan 30, 2020 at 9:14 | comment | added | user2316602 | @MattF. there is at least one obvious answer lurking nearby and I made it obvious by an edit. Please reconsider the vote to close :-) | |
| Jan 30, 2020 at 9:13 | history | edited | user2316602 | CC BY-SA 4.0 |
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| Jan 30, 2020 at 9:08 | comment | added | user44143 | What would constitute a good answer here? There are too many levels of generality, too many things that the OP may or may not have tried, and too few examples of the distributions or desired results. Maybe there’s a clearly answerable question lurking nearby, but as it stands I am voting to close. | |
| Jan 30, 2020 at 9:05 | comment | added | user2316602 | As I explained in my comment, the example by @fedja does not work when I look at relative deviations (if X is between $(1-\epsilon )E[X]$ and $(1+\epsilon )E[X]$, so is $nX$). | |
| Jan 30, 2020 at 9:01 | comment | added | Aryeh Kontorovich | You need some quantitative control on how the dependence between your variables. As @fedja's example shows, without such assumptions you get trivialities. | |
| Jan 30, 2020 at 8:56 | comment | added | user2316602 | Thank you for the response. I have updated the question. I also updated it to make clear that I care about the relative deviations. This means that in the case of identical random variables, I can just get bound on one of them and the same bound applies to their sum. | |
| Jan 30, 2020 at 8:53 | history | edited | user2316602 | CC BY-SA 4.0 |
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| Jan 29, 2020 at 21:10 | comment | added | fedja | The worst case scenario seems to be when all variables are just identical (so you have $nX$ instead of $X$ with obvious rescaled concentration bounds). Will that be good enough for you or you want more? (In the latter case some information about the nature of dependence would be necessary). It would also be nice to tell us a bit more about the setup: are your variables identically distributed, for instance? | |
| Jan 29, 2020 at 11:00 | review | First posts | |||
| Jan 29, 2020 at 11:45 | |||||
| Jan 29, 2020 at 10:58 | history | edited | user2316602 | CC BY-SA 4.0 |
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| Jan 29, 2020 at 10:57 | history | undeleted | user2316602 | ||
| Jan 29, 2020 at 10:54 | history | deleted | user2316602 | via Vote | |
| Jan 29, 2020 at 10:52 | history | asked | user2316602 | CC BY-SA 4.0 |