Timeline for Conditional Expectation / Estimator Confusion
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
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| Oct 23, 2012 at 20:56 | history | post merged (destination) | |||
| Oct 23, 2012 at 20:52 | comment | added | gui11aume | @gung Oh yes, totally!! Good observation. | |
| Oct 23, 2012 at 20:28 | answer | added | gui11aume | timeline score: 2 | |
| Oct 23, 2012 at 19:11 | comment | added | whuber♦ | @xardox Of course you cannot edit the question: you are not klingzon! The two accounts use different identifiers. If both you and klingzon verify you are the same person, a moderator can merge your accounts and then you'll be fine. | |
| Oct 23, 2012 at 18:12 | history | edited | gung - Reinstate Monica | CC BY-SA 3.0 |
updated w/ info posted incorrectly in an answer
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| Oct 23, 2012 at 17:15 | comment | added | xardox | I'm unable to edit my original question. I'm mostly confused about how to write out E[d~ | T] or E[|X1| | T] and begin to work through the algebra | |
| Oct 23, 2012 at 16:35 | comment | added | whuber♦ | As a hint, one powerful (and historically early) approach uses geometrical reasoning. Upon recognizing that, conditional on $T$, the vector $(X_1,X_2,X_3)$ is uniformly distributed on a sphere of radius $\sqrt{T}$, it's easy to see that the two parts of the question are very closely related (the second part immediately answers the first part) and the $1/2$ in the second part is the average height of a random point on the upper hemisphere of a unit sphere. This is illustrated at stats.stackexchange.com/questions/7977 and further discussed at stats.stackexchange.com/questions/22764 | |
| Oct 23, 2012 at 16:20 | review | First posts | |||
| Oct 23, 2012 at 16:56 | |||||
| Oct 23, 2012 at 16:19 | comment | added | whuber♦ | Given that $\hat{d}$ is a function of $T$, it is evident that both expectations are (non-trivial) functions of $T$. If you did not condition on $T$ and took an expectation, it would be nonsensical for $T$ to enter in the formula, wouldn't it? I realize this might not help one's intuition, but surely it shows a clear difference between conditioning on $T$ and not conditioning on it. | |
| Oct 23, 2012 at 16:15 | history | edited | whuber♦ | CC BY-SA 3.0 |
added 120 characters in body; edited tags
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| Oct 23, 2012 at 16:04 | history | asked | klingzon | CC BY-SA 3.0 |