Timeline for Is this extension of Hoeffding's inequality known?
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
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| Nov 8, 2016 at 17:14 | comment | added | PThomasCS | @AryehKontorovich I've since checked - all of the steps do hold for one-sided random variables. An updated derivation with more details is here. | |
| Aug 2, 2016 at 14:54 | comment | added | Aryeh Kontorovich | There's quite a bit of interest in concentration inequalities for unbounded (or semi-unboudned) random variables. See the related work section here, for example: jmlr.org/proceedings/papers/v32/kontorovicha14.html | |
| Aug 2, 2016 at 14:30 | comment | added | PThomasCS | @AryehKontorovich For continuous distributions, yes---we only require that $X_i \geq a$. I am not sure for non-continuous distributions though, because I am not familiar with the details of Diouf and Dufour's argument (Proposition 2) for why Anderson's inequality extends to non-continuous random variables, and so I don't know if it causes the requirement that $b$ exists to return. I'll look into this after work today. | |
| Aug 2, 2016 at 13:26 | comment | added | Aryeh Kontorovich | Since $b$ does not explicitly appear in the bound, does it follow that it holds for one-sidedly unbounded random variables? | |
| Aug 2, 2016 at 13:20 | comment | added | PThomasCS | @OriGurel-Gurevich Not in the lower bound in the original post. In the upper bound, $b$ remains but you can replace $a$ with the minimum (see the document I linked in my response to Iosif). | |
| Aug 2, 2016 at 8:11 | comment | added | Ori Gurel-Gurevich | Can you replace $a$ with the minimum? | |
| Aug 2, 2016 at 5:17 | comment | added | PThomasCS | I've uploaded it here. I hesitate to call it a different inequality from Anderson's - it's really just putting his in a different form (which requires loosening it slightly). | |
| Aug 2, 2016 at 4:46 | comment | added | Iosif Pinelis | This does look interesting and somewhat surprising, and Anderson's paper seems very nice. Is your derivation of your inequality from Anderson's result available? | |
| Aug 2, 2016 at 4:16 | comment | added | PThomasCS | It is true - it follows from Anderson's 1969 concentration inequality. I needed to put Anderson's bound into the form of Hoeffding's inequality for something I'm doing, and I got this result after loosening Anderson's bound a bit. I was surprised by this result and couldn't find it online. I'm curious whether this is known / if it's surprising to others / if I can just reference someone else to state this rather than having to include it as a claim that is unrelated to the topic of my paper (but which I need). | |
| Aug 2, 2016 at 4:03 | comment | added | Nate Eldredge | Is the result known to you? That is, are you saying you can prove it, or do you not know whether or not it is true? | |
| Aug 2, 2016 at 2:30 | history | asked | PThomasCS | CC BY-SA 3.0 |