Timeline for Sharp approximation to expectation of a ratio of a Gaussian vector
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 10 at 21:13 | comment | added | Martin Modrák | Just one more idea, barely fleshed out - it seems that if you can bound $p_i$ from below, you can obtain a polynomial approximating $\left(1 + u \left(\frac{1}{p_i} - 1 \right)\right)^{-\frac{1}{2}}$ with constant error. Substituting that polynomial into the final integral in my answer results in nasty but apparently analytically tractable integrals, which than has constant error... | |
| Jul 10 at 18:57 | comment | added | Drew Brady | While I appreciate your response, it is clear that $\psi_i(p)$ cannot be expressed in elementary functions as soon as $n \geq 3$---it corresponds to an elliptical integral in that case. Therefore, I am truly interested in elementary approximations of the multiplicative type expressed in the post. | |
| Jul 10 at 18:56 | comment | added | Martin Modrák | Just letting you now that I have substantially corrected and expanded my answer - although I wasn't able to get full solution, I think I came close, maybe you can make the next step. I am done with editing for the foreseeable future. | |
| Jul 10 at 10:15 | answer | added | Martin Modrák | timeline score: 1 | |
| Jul 9 at 1:31 | history | asked | Drew Brady | CC BY-SA 4.0 |