Timeline for Bounding the tail of an average using the the tail of individual members
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 28, 2013 at 4:08 | comment | added | Bullmoose | @Skoro Are there random variables whose tails decay exponentially that have infinite (or undefined) variance? | |
| Nov 28, 2013 at 4:07 | comment | added | Bullmoose | @Waldemar Been working with your suggestion before going away for a few days... Haven't gotten the result I need yet. Didn't know about the truncated Cheybyshev's inequality before, it's neat. Thanks for the pointer to the book -- I do realize it's one of the first results when one searches for "truncated Chebyshev's inequality" but it's quite good. | |
| Nov 23, 2013 at 17:45 | comment | added | Skoro | How about the following for a simple lower bound: $$P\left(\frac{1}{n}X_i - \mu_X > x\right)\geq \left[P(X_i - \mu_X > x)\right]^n.$$ This turns out to be sufficiently tight in certain cases, for instance, when $P(X_1 > x)$ goes down exponentially in $x$. | |
| Nov 23, 2013 at 14:36 | answer | added | ofer zeitouni | timeline score: 2 | |
| Nov 20, 2013 at 15:46 | answer | added | Bill Johnson | timeline score: 2 | |
| Nov 20, 2013 at 8:18 | comment | added | Waldemar | If you cannot use Chebyshev’s inequality (because of the infinite variance) you can always consider applying “truncated Chebyshev inequality” – see e.g. books.google.pl/… | |
| Nov 20, 2013 at 5:38 | history | asked | Bullmoose | CC BY-SA 3.0 |