Timeline for Maximizing the expectation of a polynomial function of iid random variables
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
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| Feb 25, 2019 at 8:13 | comment | added | user114668 | @JairoBochi Same, with max expectation $\sim 0.0138889$. Same for powers of three. I wonder what the appearance of a continuous component depends on. | |
| Feb 25, 2019 at 7:41 | comment | added | Jairo Bochi | What about the polynomial integrand $(X-Y)^2(Y-Z)^2(X-Z)^2$? (Baby squared) My experiments indicate that in this case the maximum is attained at the discrete measure equidistributed at $0$, $1/2$, $1$. | |
| Feb 24, 2019 at 21:26 | history | edited | user114668 | CC BY-SA 4.0 |
added 1 character in body
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| Feb 24, 2019 at 13:10 | history | edited | user114668 | CC BY-SA 4.0 |
better approximation
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| Feb 24, 2019 at 0:39 | history | edited | user114668 | CC BY-SA 4.0 |
reduce to truncated Hausdorff moment problem
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| Feb 23, 2019 at 21:41 | comment | added | user114668 | For the moments of the optimisation, I get an expectation of 0.061419, which is slightly higher than 503582/8204625. | |
| Feb 23, 2019 at 21:34 | comment | added | user44143 | For the distribution in my answer, I found moments of {1/2, 37/90, 11/30, 113/330, 65/198, 457/1430, 449/1430, 121/390, 4/13, 26/85, 233/765, 1471/4845}, which are higher than your moments by {0, 0.011, 0.016, 0.019, 0.020, 0.021, 0.022, 0.022, 0.022, 0.023, 0.023, 0.024}. | |
| Feb 23, 2019 at 19:50 | history | edited | user114668 | CC BY-SA 4.0 |
formulated a better answer
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| Feb 23, 2019 at 16:38 | history | edited | user114668 | CC BY-SA 4.0 |
symmetrizised f
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| Feb 23, 2019 at 0:24 | history | edited | user114668 | CC BY-SA 4.0 |
deleted 34 characters in body
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| Feb 23, 2019 at 0:17 | history | edited | user114668 | CC BY-SA 4.0 |
reconstruction with Bernstein polynomials
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| Feb 22, 2019 at 22:22 | history | answered | user114668 | CC BY-SA 4.0 |