Timeline for Good upper-bound for $\mathbb E[|X-np|^r]$ where $X \sim \text{Binomial}(n,p)$ and $r \ge 1$
Current License: CC BY-SA 4.0
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| May 29, 2019 at 15:36 | comment | added | dohmatob | Thanks for establishing the optimality of the bound. It makes the proposal very compelling. N.B.: Sorry I deleted my comment before you could post yours. | |
| May 29, 2019 at 14:37 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| May 29, 2019 at 14:27 | comment | added | Iosif Pinelis | I have now shown that the bound is the best possible. | |
| May 29, 2019 at 14:26 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| May 29, 2019 at 12:31 | vote | accept | dohmatob | ||
| May 29, 2019 at 12:31 | comment | added | dohmatob | Thanks for the nice addendum. It's really helpful. Also Bahr-Esseen is fresh news for me. Thanks. | |
| May 28, 2019 at 11:29 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| May 28, 2019 at 3:51 | comment | added | dohmatob | Hum, upvoted, but I'm afraid this is not readily exploitable. I'd expect there exists explicit bounds for such an explicit problem. [2] appears to be rather too ambitious, and I'm willing to strike a compromise. I only require a bound with a "decent" dependence on the parameters $n$, $p$, and $r$ (it may be assumed that $1 \le r \le 2$, BTW). | |
| May 28, 2019 at 3:20 | comment | added | Iosif Pinelis | @dohmatob : Yes, in [2] the bounds are quite explicit. However, they are much more general and contain a number of parameters, in which it should be straightforward to minimize, depending on how $n$ and $p$ are related in your setting. | |
| May 28, 2019 at 3:11 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| May 28, 2019 at 2:54 | comment | added | dohmatob | Thanks for the references. Can the bound be made more explicit ? I'm not away that the problem is simpler for Poisson variables. Thanks in advance. | |
| May 28, 2019 at 1:26 | history | answered | Iosif Pinelis | CC BY-SA 4.0 |