Timeline for $L_1$ norm concentration of an empirical distribution
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
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| May 16, 2023 at 21:30 | answer | added | usul | timeline score: 1 | |
| May 16, 2023 at 14:15 | history | edited | white | CC BY-SA 4.0 |
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| May 16, 2023 at 14:10 | comment | added | white | @IosifPinelis I mean concentration bound, for example like Hoeffding inequality for one-dimensional variable. Here, we want $\mathbb{P}\{\sum_{x_i\in\mathbb{X}}|\hat{P}(X=x_i)-P(X=x_i)| \leq t\} \geq 1-\delta$, where $\delta$ is a small value, and the question is what is $t$ ? | |
| May 16, 2023 at 13:59 | comment | added | Iosif Pinelis | The latter sum is a random variable. What kind of bound on it, and in what specific sense, do you want? | |
| May 16, 2023 at 13:52 | history | edited | white | CC BY-SA 4.0 |
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| May 16, 2023 at 13:51 | comment | added | white | Exactly. @kodlu | |
| May 16, 2023 at 13:47 | comment | added | kodlu | do you mean $x_i$ occurs $N_i$ times out of $N$ samples of $X$? | |
| May 16, 2023 at 13:39 | history | asked | white | CC BY-SA 4.0 |