Timeline for Expectation of the ratio of two discrete random variables with combinatorial constraints
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 4, 2020 at 19:27 | comment | added | Penelope Benenati | It's a bit complex, anyway I agree, I understood that for my goal I should use some of the constraints not mentioned in the original post above. Thank you once again! | |
| Nov 4, 2020 at 18:57 | comment | added | Mikhail Tikhomirov | Well, there's only so much to gather in the worst-case OP setting. If there's additional information that could be helpful for the estimate, please feel free to put it in another question. | |
| Nov 4, 2020 at 18:51 | vote | accept | Penelope Benenati | ||
| Nov 4, 2020 at 18:50 | comment | added | Penelope Benenati | Yes, of course. However, in the "real" research problem I am working on (which includes this little subproblem of this post here above) I have exactly $\min_i(\alpha_i)\simeq 0.8$ and $\max_i(\alpha_i)\simeq 0.9$. It would be a significant improvement to obtain an expected value of $X$ always strictly larger than $\min_i(\alpha_i)$. That's the main reason I asked my last question in the previous comment. Thank you anyway. | |
| Nov 4, 2020 at 16:50 | comment | added | Mikhail Tikhomirov | In your assumption the absolute error is $0.1 - O(1/n)$. Though, as $\min \alpha$ and $\max \alpha$ become closer, the trivial lower bound $\min \alpha$ gradually becomes "better" and the question make less and less sense. | |
| Nov 4, 2020 at 13:08 | comment | added | Penelope Benenati | Thank you for your answer @Mikhail, I see the point. Can we get a similar result in your opinion if we further assume that $\min_i(\alpha_i)$ and $\max_i(\alpha_i)$ are both close to $1$? Assume for instance that $\alpha_{i}=0.8$ for all $1\le i\le n/2$ and $\alpha_j=0.9$ for all $n/2+1\le j\le n$. I am asking this question also because I suspect that your result depends on the fact $\max_i(\alpha_i)-\min_i(\alpha_i)$ is equal to $1$ (or, more in general, it is large w.r.t the maximum possible difference value -- which is $1$). | |
| Nov 4, 2020 at 2:37 | history | edited | Mikhail Tikhomirov | CC BY-SA 4.0 |
added 9 characters in body
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| Nov 4, 2020 at 2:28 | history | answered | Mikhail Tikhomirov | CC BY-SA 4.0 |