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Results tagged with measure-concentration
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user 27773
2
votes
0
answers
316
views
McDiarmid's Inequality bounding deviation with multiplicative error?
Fix $m$ arbitrary values $x_1, x_2, ..., x_m$ in $[0,1]$, and an integer $n$. Obtain $n$-set $S$ by drawing $n \le m$ times randomly without replacement from $\{1,2,..,m\}$. Define r.v. $X = \sum_{i …
- 183
2
votes
Does Multiplicative Version of Azuma's Inequality Hold?
Yes, such bounds are possible. You can adapt the proof of Azuma's inequality to the multiplicative-error case, if you set it up correctly.
For example:
Lemma 10 [this paper].
Let $Y=\sum_{t=1}^T x_t …
- 183
1
vote
Chernoff-type bounds for a stopped sum of independent random variables
The two answers so far may give the impression that bounds in the desired spirit (Chernoff-like bounds for sums with stopping times) are not possible. But useful bounds in this spirit can indeed be s …
- 183