Timeline for Distribution of inverse Wishart to a power?
Current License: CC BY-SA 3.0
15 events
| when toggle format | what | by | license | comment | |
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| Jun 17, 2023 at 21:01 | answer | added | japalmer | timeline score: 1 | |
| Sep 24, 2022 at 21:44 | comment | added | John Jiang | Any motivation for this question? | |
| Feb 3, 2021 at 16:17 | history | edited | kjetil b halvorsen♦ |
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| Apr 13, 2017 at 12:44 | history | edited | CommunityBot |
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| May 9, 2012 at 23:16 | history | notice removed | CommunityBot | ||
| May 9, 2012 at 23:16 | history | bounty ended | CommunityBot | ||
| May 3, 2012 at 17:20 | comment | added | shabbychef | Maybe there is an approach via the eigenvalues and eigenvectors of $A$, perhaps using the Marchenko Pastur distribution. | |
| May 3, 2012 at 4:51 | comment | added | shabbychef | @cardinal I suspect you are right, and had tried the same trick, but instead assuming wlog that $\ell$ was the vector of all ones, hoping it would lead to the trace of $A^{-m}$. It did not, though. | |
| May 3, 2012 at 0:41 | comment | added | cardinal | I think we can reduce the problem considerably (please check, though). Note that the reciprocal of your quantity of interest is completely invariant to orthogonal transformations of $\ell$, so without loss of generality we can take $\ell = e_1$. Thus, your question amounts to finding the marginal distribution of the reciprocal of (any) of the diagonal entries of $A^{-m}$. The standard proof in the $m = 1$ case effectively uses this fact and I think a connection between invariance under group actions of $O(n,\mathbb R)$ and independence can be drawn, but I haven't worked out the details (yet). | |
| May 2, 2012 at 22:11 | comment | added | shabbychef | @StasK is there a Bartlett-type decomposition for the inverse-Wishart? I only know the one for the Wishart. | |
| May 2, 2012 at 21:51 | comment | added | StasK | Is Bartlett decomposition of any help? | |
| May 1, 2012 at 23:13 | history | tweeted | twitter.com/#!/StackStats/status/197463837149102081 | ||
| May 1, 2012 at 21:21 | history | notice added | shabbychef | Authoritative reference needed | |
| May 1, 2012 at 21:21 | history | bounty started | shabbychef | ||
| Apr 27, 2012 at 22:58 | history | asked | shabbychef | CC BY-SA 3.0 |