Timeline for Violating an order statistic inequality?
Current License: CC BY-SA 4.0
19 events
| when toggle format | what | by | license | comment | |
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| Jan 3, 2023 at 3:05 | comment | added | Bill Bradley | (I suppose, as things get asymptotically small, the mode must eventually win.) | |
| Jan 3, 2023 at 3:04 | history | edited | Bill Bradley | CC BY-SA 4.0 |
Adding strangely missing inversion.
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| Jan 3, 2023 at 2:59 | comment | added | Bill Bradley | I know, right? Unfortunately, @Henry, the $\frac{i}{n}$ seems to be the standard definition. I asked essentially your question on CrossValidated recently: stats.stackexchange.com/questions/599678/… . I think there are reasonable arguments for using the mode (from a confidence interval perspective), although if you want to minimize the epsilon above, my handful of experiments suggests that the mean is the best (i.e., supports a smaller $\varepsilon$ than the "classical", the mode and the median-ish). | |
| Jan 3, 2023 at 0:05 | comment | added | Henry | $\frac in$ looks biased upwards. $q_i \sim \text{Beta}(i,n-i+1)$ so the expected value of $q_i$ is $\frac{i}{n+1}$, the most-likely/mode/highest-density value is $\frac{i-1}{n-1}$ for $n>1$, and the median is about $\frac{i-\frac13}{n+\frac13}$ for $1 < i <n$ | |
| Dec 31, 2022 at 16:40 | history | edited | Michael Hardy | CC BY-SA 4.0 |
added 22 characters in body
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| Dec 31, 2022 at 16:11 | history | edited | Michael Hardy | CC BY-SA 4.0 |
added 5 characters in body
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| Dec 31, 2022 at 16:09 | comment | added | Bill Bradley | Thank you, @MichaelHardy, I've fixed that. | |
| Dec 31, 2022 at 16:09 | history | edited | Bill Bradley | CC BY-SA 4.0 |
Correcting use of "sample".
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| Dec 31, 2022 at 16:07 | comment | added | Michael Hardy | The standard way in which the word "sample" is used in statistics would refer to "a sample of $n$ i.i.d. observations" rather than to "$n$ i.i.d. samples". For example, the thing that in standard usage is called a "two-sample t-test" obviously does not rely on just two independent observations, and what would the term "sample size" mean? | |
| Dec 31, 2022 at 14:36 | history | edited | Bill Bradley | CC BY-SA 4.0 |
Adding a clarifying comment to the code per JohnJiang's suggestion.
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| Dec 31, 2022 at 14:32 | comment | added | Bill Bradley | Ah, @JohnJiang, I believe that it's correct as it stands, but that touches on the mistake I made. (See the comments below Iosef Pinelis' solution below.) But the ambiguity there is what killed me; I'll add a comment to make it clearer. | |
| Dec 31, 2022 at 6:21 | comment | added | John Jiang | In your definition of prob_true did you have a reversed inequality sign? | |
| Dec 31, 2022 at 0:07 | history | edited | Michael Hardy | CC BY-SA 4.0 |
added 13 characters in body
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| Dec 30, 2022 at 16:12 | vote | accept | Bill Bradley | ||
| Dec 30, 2022 at 16:12 | history | edited | Bill Bradley | CC BY-SA 4.0 |
explained how to fix the problem
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| Dec 29, 2022 at 22:16 | review | Close votes | |||
| Jan 3, 2023 at 3:05 | |||||
| Dec 29, 2022 at 21:57 | history | edited | YCor | CC BY-SA 4.0 |
formatting, added tag
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| Dec 29, 2022 at 21:22 | answer | added | Iosif Pinelis | timeline score: 5 | |
| Dec 29, 2022 at 20:45 | history | asked | Bill Bradley | CC BY-SA 4.0 |