Timeline for Concentration inequalities for the maximum of the rescaled/normalized sum of iid random variables
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
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| Sep 24, 2019 at 8:49 | comment | added | Davide Giraudo | Indeed, there was a typo. The proofs works in the same way as for Doob's inequality. I also made the reference more precise. | |
| Sep 24, 2019 at 8:48 | comment | added | Thomas Dybdahl Ahle | Concerning only the second term, it seems that if all $\mathbb E[S_i^2]=i$, we need $c_i^2\approx i \log i$ to get a probability below 1. This seems similar to the answer of @Mark, but worse than the $\sqrt{\log\log n}$ answer by Tanguy. (Just for my own understanding and comparison) | |
| Sep 24, 2019 at 8:48 | history | edited | Davide Giraudo | CC BY-SA 4.0 |
added 58 characters in body
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| Sep 24, 2019 at 8:41 | comment | added | Thomas Dybdahl Ahle | Should the $c_n^p$ on the right-hand side be in the denominator? It seems that if we scale the $S_k$ down by a larger factor, the probability that they exceed some value should decrease rather than increase. I would check the paper, but it doesn't seem to have a Theorem 1, so I'm not really sure. | |
| Nov 3, 2013 at 11:47 | vote | accept | Adrien | ||
| Nov 3, 2013 at 11:47 | vote | accept | Adrien | ||
| Nov 3, 2013 at 11:47 | |||||
| Oct 31, 2013 at 10:51 | history | edited | Davide Giraudo | CC BY-SA 3.0 |
deleted 9 characters in body
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| Oct 31, 2013 at 10:17 | comment | added | Adrien | Thanks for the answer. I didn't know about this generalization of the Hajek-Renyi inequality. I need to think about it to see if it can be generalized further with exponential functions. | |
| Oct 30, 2013 at 19:18 | history | edited | Davide Giraudo | CC BY-SA 3.0 |
I missed the $\max$.
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| Oct 30, 2013 at 12:39 | history | answered | Davide Giraudo | CC BY-SA 3.0 |