Timeline for Does minimum mean-square error characterize distribution?
Current License: CC BY-SA 4.0
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| when toggle format | what | by | license | comment | |
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| Oct 20, 2021 at 1:40 | comment | added | jlewk | Tweedie's formula gives explicit expressions for the conditional mean $E[X|X_t]$ and variance $Var[X|X_t]$. These can be expressed in terms of the first and second derivatives of $\log f$ takien at $X_t$ where $f$ the density of $X$. If you know $R(t)=E[Var[X|X_t]]$, taking derivatives a $0^+$ (and maybe the Taylor expansion of $R(t)$ at 0) should provide information about certain moments of the derivatives of $f$. I don't know if that will be sufficient to characterize the distribution of $X$. | |
| S Oct 18, 2021 at 13:10 | review | First questions | |||
| Oct 18, 2021 at 13:15 | |||||
| S Oct 18, 2021 at 13:10 | history | asked | Ted Gilbraith | CC BY-SA 4.0 |