Timeline for On estimating Covariance between a random variable and its non-linear transform
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 20, 2021 at 20:20 | vote | accept | Trade Paul | ||
| Mar 20, 2021 at 19:45 | answer | added | Carlo Beenakker | timeline score: 2 | |
| Mar 20, 2021 at 19:34 | comment | added | Trade Paul | No, it need not be zero mean. In fact, if the mean is negative, or zero, the non-negativeness emerges trivially from the definition : $ cov(X, R(X)) = E[X.R(X) ] - E[X]E[R(x)]$. Because $E[R(x)]$ is always non-negative. But I can't figure out the case for $E[X] > 0$. | |
| Mar 20, 2021 at 19:24 | comment | added | rubikscube09 | If $X$ is mean zero then I believe $\mathrm{Cov}(X,R(X)) = \int_\Omega X(\omega) R(X(\omega))d\mathbb{P}(\omega) = \int_{X>0} (X(\omega))^2 d\mathbb{P}(\omega) \geq 0$ | |
| Mar 20, 2021 at 19:21 | review | First posts | |||
| Mar 20, 2021 at 19:55 | |||||
| Mar 20, 2021 at 19:16 | history | asked | Trade Paul | CC BY-SA 4.0 |