Timeline for Textbook default estimator of Bernoulli variance
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
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| May 18, 2022 at 3:00 | history | tweeted | twitter.com/StackStats/status/1526759558798094336 | ||
| May 18, 2022 at 0:19 | comment | added | kjetil b halvorsen♦ | See the related stats.stackexchange.com/questions/61815/…, stats.stackexchange.com/questions/83033/… | |
| Jan 21, 2021 at 22:37 | comment | added | Markus Loecher | Thanks again, especially for the reminder that Bernoulli/Binomial are one-parameter distributions, which I agree is relevant for my question. | |
| Jan 19, 2021 at 14:04 | comment | added | whuber♦ | I think it might depend on the application, Markus. I would keep an eye out for statistical procedures that appear to involve factors that are functions of $(n-1)/n,$ because that would suggest they could be simplified by using the unbiased estimator. But unless the target of estimation is $p(1-p)$ itself, it is hard to see how adjusting for the bias would be relevant to most statistical procedures. In particular, you cannot simultaneously estimate $p$ and $p(1-p)$ in an unbiased way. | |
| Jan 19, 2021 at 10:18 | comment | added | Markus Loecher | @whuber Thank you for this VERY helpful and wise inferential perspective which would explain the limited upsides. I still wonder what the downside of using the unbiased version would be. Is it simply that p*(1-p) is so concise and elegant compared to p*(1-p)*n/(n-1)? | |
| Jan 17, 2021 at 18:46 | comment | added | whuber♦ | In most other cases, the test statistics based on the uncorrected estimator would follow distributions that are more complicated or onerous to tabulate, whereas that's not an issue in the Bernoulli case. Consideration of the tests for OLS, for instance, shows how one set of tables of t statistics will suffice provided the error variance is corrected by dividing by $n-p$ rather than $n$ itself. | |
| Jan 17, 2021 at 18:11 | history | edited | kjetil b halvorsen♦ |
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| Jan 17, 2021 at 12:38 | comment | added | seanv507 | could you give at least one examples of the textbooks? | |
| Jan 17, 2021 at 11:34 | history | asked | Markus Loecher | CC BY-SA 4.0 |