Timeline for On concentration of a sum random variable
Current License: CC BY-SA 3.0
17 events
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| Oct 3, 2017 at 0:32 | history | edited | Iosif Pinelis | CC BY-SA 3.0 |
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| Oct 2, 2017 at 20:58 | history | edited | Iosif Pinelis | CC BY-SA 3.0 |
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| Oct 2, 2017 at 19:06 | history | edited | Iosif Pinelis | CC BY-SA 3.0 |
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| Oct 2, 2017 at 18:07 | history | edited | Iosif Pinelis | CC BY-SA 3.0 |
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| Oct 2, 2017 at 17:35 | history | edited | Iosif Pinelis | CC BY-SA 3.0 |
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| Oct 2, 2017 at 15:59 | comment | added | Turbo | one way to think of them is as packaging correlated data ($v_iv_j$) in a suitable way $u_{ij}$ so that the resulting package is compact and if I send enough of such packages we can recover the data ($v_iv_j$) information theoretically. Under what suitable scaling can we expect the information sent to not exceed the useful information sent by a big amount? | |
| Oct 2, 2017 at 15:54 | comment | added | Turbo | They are discrete and they could be dependent.. it is just hard to say.. I just want to know what necessary and sufficient conditions if we force on them we can get overwhelming cancellations. | |
| Oct 2, 2017 at 15:54 | comment | added | Iosif Pinelis | Perhaps you can just tell us what the $u_{ij}$'s actually are in your particular research problem. | |
| Oct 2, 2017 at 15:52 | comment | added | Turbo | It still does not rule out all conditions but only what we think should be natural. I am just looking for plausible natural ways to look where cancellations are the overwhelming rule. I think it is a fair problem. The conditions should be interesting. | |
| Oct 2, 2017 at 15:50 | comment | added | Turbo | It will be awkward if I have a different post for asymptotics on same theme.. but I can do that once the current post in well answered. | |
| Oct 2, 2017 at 15:50 | comment | added | Iosif Pinelis | I think my answer suggests that the lower bound $1-\frac1{n^2}$ on that probability will be impossible under any reasonable broad conditions. Indeed, why would reasonable broad conditions exclude the case considered in my answer? | |
| Oct 2, 2017 at 15:41 | comment | added | Turbo | It does not answer 'Under what broad conditions on distribution of $r$ can above probability be $>1-\frac1{n^2}$?'. Actually it is clear I am looking for asymptotics from my attempt with Chebyshev inequality. | |
| Oct 2, 2017 at 15:40 | comment | added | Iosif Pinelis | That is indeed quite a different question, and you can post it separately. I think it will be right if you restore the original question in this post. I don't understand why you say my answer to your original question is only partial. | |
| Oct 2, 2017 at 15:37 | comment | added | Turbo | I see what you say.... then this is one partial answer.... could you also state how fast it approaches $0$? | |
| Oct 2, 2017 at 15:36 | comment | added | Iosif Pinelis | Your conditions do not exclude $u_{ij}=t_i t_j$, do they? | |
| Oct 2, 2017 at 15:30 | comment | added | Turbo | why $u_{ij}=t_it_j$? $u_{ij}$ are not in product form and $u_{ij}$ could be independent of each other (I only said might not be independent) and so we cannot force conditional dependence. | |
| Oct 2, 2017 at 15:27 | history | answered | Iosif Pinelis | CC BY-SA 3.0 |