Timeline for Tail bound for maximum of independent (but not identical) binomial random variables

12 events

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Apr 13, 2017 at 12:58	history	edited	CommunityBot		replaced http://mathoverflow.net/ with https://mathoverflow.net/
Mar 9, 2017 at 4:28	history	edited	stats134711	CC BY-SA 3.0	edited body
Mar 9, 2017 at 3:23	comment	added	usul		Continuing Fedor's line of reasoning, we can use Chernoff-type bounds to obtain $P(X_i \leq c) \leq e^{-f(c,p_i,n)}$, so the probability is at least $1 - \exp\left[ - \sum_{i=1}^m f(c,p_i,n) \right]$. For example, I think Hoeffding's gives $f(c,p_i,n) = 2(c - np_i)^2/n$.
Mar 8, 2017 at 21:44	vote	accept	stats134711
Mar 8, 2017 at 21:21	answer	added	Rodrigo Ribeiro		timeline score: 1
Feb 23, 2017 at 15:52	comment	added	stats134711		That was the first step I tried but I'm having trouble getting anywhere productive for successive calculations.
Feb 23, 2017 at 5:50	comment	added	Fedor Petrov		Of course it depends on $p_i$, if all $p_i$ are almost 0, this probability is small. We have $P(\max_{1\leq i\leq m} X_i > c)=1-\prod_{1\leq i\leq m}P(X_i\leq c)$, this should be useful for formulating concrete results
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Feb 23, 2017 at 2:05	history	edited	stats134711	CC BY-SA 3.0	added 30 characters in body
Feb 23, 2017 at 1:52	history	asked	stats134711	CC BY-SA 3.0