Timeline for Cramér–Rao type bound for absolute estimation error
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
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| Nov 1 at 22:23 | history | edited | LSpice | CC BY-SA 4.0 |
Cramer -> Cramér, Holder -> Hölder, while this is on the front page
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| Dec 5, 2015 at 20:15 | comment | added | Sealander | You are right. I have replaced the inequality with Holder's inequality and followed it through to what I think is a nice result. The shakiest part is now the limit where $q \rightarrow \infty$, but I think it is valid (see $\ell_\infty$ norms) | |
| Dec 5, 2015 at 20:12 | history | edited | Sealander | CC BY-SA 3.0 |
Replaced erroneous inequality with Holder's inequality and followed it through
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| Nov 24, 2015 at 19:26 | comment | added | Michael | Note that: $$E[|G|^2]=E[|G|]^2 \iff Var(|G|)=0 \iff \mbox{$|G|$ is constant with prob 1}$$ | |
| Nov 24, 2015 at 11:42 | history | edited | Sealander | CC BY-SA 3.0 |
Typo
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| Nov 24, 2015 at 11:16 | comment | added | Sealander | The inequality was kind of a shot in the dark and the more I think about it, the more I don't think it holds even if you restrict it to zero-mean random variables. | |
| Nov 24, 2015 at 10:09 | comment | added | Sealander | I am definitely on weakest ground regarding the inequality, but taking your special case of $G = H$ reduces to $E[G^2] \leq E[|G|]^2$ (keeping the absolute value) which seems like it might hold conditionally on $E[G] = 0$. | |
| Nov 24, 2015 at 4:24 | comment | added | Michael | Well, your absolute value inequality does not hold in general. For random variables $G,H$, it reduces to the claim $|E[GH]| \leq E[|G|]E[|H|]$. But let $G=H$ and let $G$ be a nonnegative random variable. This reduces to $E[G^2] \leq E[G]^2$, but this is violated whenever $G$ has nonzero variance. | |
| Nov 24, 2015 at 4:12 | comment | added | Michael | Thanks for your interest! I asked this 6 months ago, so I need to recall my line of thought on this problem. I will read over your answer this week when I get a chance. | |
| Nov 23, 2015 at 23:12 | history | answered | Sealander | CC BY-SA 3.0 |