Timeline for $\mathbb{E}[X^4]=1$, $X,Y$ iid, what's the best upper bound of $\mathbb{E}[(X-Y)^4]$?
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
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| Apr 30, 2018 at 4:01 | vote | accept | Chen Dan | ||
| Apr 29, 2018 at 12:09 | history | edited | Iosif Pinelis | CC BY-SA 3.0 |
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| Apr 29, 2018 at 12:07 | comment | added | Iosif Pinelis | I have added an elementary solution, without using Mathematica. | |
| Apr 29, 2018 at 12:03 | history | edited | Iosif Pinelis | CC BY-SA 3.0 |
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| Apr 29, 2018 at 6:01 | comment | added | Will Sawin | Note that your formula is $\operatorname{trace}(M D MD)$ where $D$ is a matrix with alternating plus and minus signs. The same works for the analogous problem with $(X-Y)^{2\ell}$. However, I wasn't able to use this idea to solve the analogous problem. | |
| Apr 29, 2018 at 3:42 | history | edited | Iosif Pinelis | CC BY-SA 3.0 |
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| Apr 29, 2018 at 3:19 | history | edited | Iosif Pinelis | CC BY-SA 3.0 |
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| Apr 29, 2018 at 3:13 | history | answered | Iosif Pinelis | CC BY-SA 3.0 |