Timeline for Expectation of a simple function of multivariate gaussians iid rvs
Current License: CC BY-SA 3.0
13 events
| when toggle format | what | by | license | comment | |
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| Jul 29, 2014 at 22:01 | history | edited | Ricardo Andrade | CC BY-SA 3.0 |
replaced tag 'tag-removed'
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| Jan 8, 2013 at 2:36 | vote | accept | gappy3000 | ||
| Aug 20, 2011 at 22:34 | answer | added | Did | timeline score: 7 | |
| Aug 20, 2011 at 15:21 | answer | added | Brendan McKay | timeline score: 6 | |
| Sep 24, 2010 at 16:40 | comment | added | Suvrit | Is your integral by any chance related to the Bingham distribution? | |
| Sep 10, 2010 at 19:21 | comment | added | Will Jagy | Thanks, Didier. No sorrow necessary. | |
| Sep 10, 2010 at 19:02 | comment | added | Did | Will, the formula you wrote above is the natural generalization of the formula for $n=2$. Unfortunately the trick I used to prove the $n=2$ case fails for larger values of $n$ and since, at this moment, I see no "geometrical" reason (whatever that means) pointing to the $\ell^1$ norm, the answer to your question is: I do not know. Sorry. | |
| Sep 10, 2010 at 17:15 | comment | added | Will Jagy | Didier, if we demand all $ \lambda_j > 0$ and put $ \lambda_i^2$ in the numerator to make the sum to 1 obvious, do you think $$ E\left( \frac{ \lambda_i^2 X_i^2}{\sum_j \lambda_j^2 X_j^2}\right) = \frac{ \lambda_i}{\sum_j \lambda_j}? $$ | |
| Sep 10, 2010 at 16:12 | comment | added | Did | Funny: for two random variables $E(X^2_1/(\lambda^2_1X^2_1+\lambda^2_2X_2^2))=1/(|\lambda_1|(|\lambda_1|+|\lambda_2|))$. I wonder why the $\ell^1$ norm enters the picture here... | |
| Sep 10, 2010 at 9:05 | answer | added | Darsh Ranjan | timeline score: 1 | |
| Sep 10, 2010 at 0:37 | comment | added | Will Jagy | Do you have some part answers, say estimates or upper or lower bounds, with only two variables but unequal $\lambda_j$? For instance $\lambda_1=1$ but $\lambda_2$ very large, what happens approximately? | |
| Sep 9, 2010 at 22:00 | history | edited | gappy3000 | CC BY-SA 2.5 |
deleted 1 characters in body
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| Sep 9, 2010 at 16:51 | history | asked | gappy3000 | CC BY-SA 2.5 |