Timeline for Can we find the following $k$ so that the following inequality holds for asymptotic normal?
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 8, 2022 at 16:12 | comment | added | Iosif Pinelis | @Hermi : I never assumed or said that the random vector $u$ is the same as the true, non-random vector $e_1$. As I wrote, by the spherical symmetry, the conditional distribution of $(X_1,\dots,X_k)$ given $u$ does not depend on the value of $u$. So, we can choose any particular value of $u$ on the unit sphere; $e_1$ is one of those values. (It is not a good idea to denote random variables/elements by lower-case letters; lower-case letters should be used for values of random variables/elements.) | |
| Dec 8, 2022 at 4:38 | comment | added | Hermi | Thank you! But why did you assume that $u=e_1$? I feel that without this hypothesis, we are still being led by $\frac{X_1^2+\dots+X_k^2}{X_1^2}\to\frac{G_1^2+\dots+G_k^2}{G_1^2}$ in distribution. | |
| Dec 8, 2022 at 4:23 | vote | accept | Hermi | ||
| Dec 8, 2022 at 2:19 | history | answered | Iosif Pinelis | CC BY-SA 4.0 |