Timeline for multivariate Gaussian approximation in total variation distance
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
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| Feb 4, 2016 at 14:16 | comment | added | Mark Meckes | Incidentally, the OP's question suggests that they might be familiar with arxiv.org/abs/math/0606073, from which you can see that I know perfectly well that Stein's method can be used to derive total variation bounds. | |
| Feb 4, 2016 at 14:11 | comment | added | Mark Meckes | @Guillaume: You seem to have misread what I wrote. What I said is that total variation approximation is simply false without some kind of additional assumptions, so it is equally out of reach for any method. This is the kind of "impossibility result" the OP asked about. On the other had, if you do have appropriate additional assumptions, then Stein's method is often the best way to reach total variation bounds. | |
| Feb 4, 2016 at 10:25 | comment | added | Guillaume Dehaene | Stein's method can be used to derive total-variation bounds. This is because $d_{TV}(p_1,p_2) = max_{||h|| \leq 1} (E_{p_1}(h) - E_{p_2}(h) )$. The properties of the solution of the "Stein differential equation" for gaussian approximation in 1D are given in Lemma 2.4 of Chen, Goldstein, Shao (2011). | |
| Apr 27, 2012 at 22:23 | history | answered | Mark Meckes | CC BY-SA 3.0 |