Timeline for Minimum and maximum bound on mean of product of three pairwise uncorrelated random variables
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 21, 2015 at 20:47 | comment | added | A.S. | @Kevin Not anything per se. This shows that Holder's bound $|E(XYZ)|\le (E(|X|^3)E(|Y|^3)E(|Z|^3))^{1/3}$ is tight. | |
| Dec 20, 2015 at 17:13 | comment | added | Kevin P. Costello | Modified version of this: Let $\eta_1$ and $\eta_2$ be independent, and set $\eta_3=\eta_1 \eta_2$. The variables are still uncorrelated, but now $E(XYZ)=E(\xi^3)$. Even if $E(\xi^3)$ is finite, it could be anything. | |
| Dec 20, 2015 at 16:49 | comment | added | Serguei Popov | Then I don't know. Maybe, play with inequalities like $\frac{1}{3}(|XY|+|YZ|+|XZ|)\geq |XYZ|^{2/3}$?.. | |
| Dec 20, 2015 at 16:42 | comment | added | Acapello | Ok, and if we also assume that $E(XYZ)$ exist? | |
| Dec 20, 2015 at 16:40 | history | answered | Serguei Popov | CC BY-SA 3.0 |