Timeline for Best estimator of the mean of a normal distribution based only on box-plot statistics
Current License: CC BY-SA 4.0
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| Aug 3, 2023 at 21:42 | comment | added | Glen_b | Added a section in note [1] to hopefully explain it further. In short, we're trying to minimize the variance of an (unbiased) linear combination of order statistics, and at given $n$, that variance is quadratic in $q$ (but the coefficients are themselves functionals of the standard normal density, and those terms involve $n$). This is all doable, and would be fairly straightforward to code, it just takes time to set it up properly. The asymptotic case is somewhat easier to deal with but still takes some calculation. I hope to come back and add some more. If time permits I'll show a calculation | |
| Aug 3, 2023 at 21:39 | history | edited | Glen_b | CC BY-SA 4.0 |
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| Aug 3, 2023 at 6:04 | comment | added | user225256 | Will you elaborate on the comment that “asymptotically the median and midhinge will combine linearly (due to their joint normality)”? How do we rule out something like $(1-q)M+qH$ with $q=(Q_3-2Q_2+Q_1)^2/(Q_3-Q_1)^2$? That function would emphasize the median more when the median and midhinge are close, and emphasize the midhinge more when the median and midhinge are far apart. | |
| Jul 28, 2023 at 2:54 | history | edited | Glen_b | CC BY-SA 4.0 |
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| Jul 28, 2023 at 1:50 | history | edited | Glen_b | CC BY-SA 4.0 |
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| Jul 26, 2023 at 0:20 | history | edited | Glen_b | CC BY-SA 4.0 |
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| Jul 25, 2023 at 23:08 | history | edited | Glen_b | CC BY-SA 4.0 |
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| Jul 25, 2023 at 17:11 | history | edited | Glen_b | CC BY-SA 4.0 |
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| Jul 25, 2023 at 15:10 | history | edited | Glen_b | CC BY-SA 4.0 |
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| Jul 25, 2023 at 13:50 | history | edited | Glen_b | CC BY-SA 4.0 |
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| Jul 25, 2023 at 13:20 | history | edited | Glen_b | CC BY-SA 4.0 |
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| Jul 25, 2023 at 13:12 | history | edited | Glen_b | CC BY-SA 4.0 |
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| Jul 25, 2023 at 8:14 | comment | added | Glen_b | Note to self; add a brief mention of ncbi.nlm.nih.gov/pmc/articles/PMC9621295 | |
| Jul 25, 2023 at 8:00 | history | edited | Glen_b | CC BY-SA 4.0 |
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| Jul 25, 2023 at 7:17 | history | edited | Glen_b | CC BY-SA 4.0 |
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| Jul 25, 2023 at 6:52 | history | edited | Glen_b | CC BY-SA 4.0 |
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| Jul 25, 2023 at 6:31 | history | edited | Glen_b | CC BY-SA 4.0 |
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| Jul 25, 2023 at 6:23 | history | answered | Glen_b | CC BY-SA 4.0 |