Timeline for Berry-Esseen type bounds for functions of almost Gaussian random variables
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
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| Apr 16, 2021 at 21:17 | comment | added | 61plus | I see what is going on now. The continuous mapping theorem will require some form of convergence of joint distribution as well. Thank you for the counterexample. | |
| Apr 16, 2021 at 20:47 | comment | added | Will Sawin | That's not good enough. For example we can take $X_1$ and $X_2$ to be Gaussian but $X_1=X_2 $ half the time and $X_1=-X_2$ half the time. Then $\mathbb E[X_1X_2]=0$ but $X_1,X_2$ are very different from the standard Gaussians $Z_1,Z_2$ with the same mean and variance. | |
| Apr 16, 2021 at 20:15 | history | edited | 61plus | CC BY-SA 4.0 |
added 28 characters in body
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| Apr 16, 2021 at 20:12 | comment | added | 61plus | I intended for the first inequality to be univariate and true for all $i$. An example of $\rho(x)$ could be like $\varepsilon/(1+x^2)$. | |
| Apr 16, 2021 at 19:29 | comment | added | Will Sawin | Is the maximum value of $\rho$ small, or do you want to take advantage of the fact that it decreases? Is the first inequality supposed to be multidimensional, with $x$ a vector in $\mathbb R^n$? If not, won't you run into trouble even with $\rho=0$? | |
| Apr 16, 2021 at 17:35 | history | edited | 61plus |
edited tags
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| Apr 16, 2021 at 16:54 | history | asked | 61plus | CC BY-SA 4.0 |