Timeline for Why is the t-test designed for small samples?
Current License: CC BY-SA 4.0
14 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 30, 2021 at 19:43 | comment | added | Richard Hardy | A short answer can be great as long as it is not incorrect. Going to the second paragraph, $\hat\sigma=\sigma$ is incorrect. We have convergence getting us towards that result asymptotically but it is never correct in practice (given a finite sample). | |
| Jan 30, 2021 at 19:20 | history | edited | Aksakal | CC BY-SA 4.0 |
edited body
|
| Jan 30, 2021 at 19:20 | comment | added | Aksakal | I think given the question phrasing is better to simplify the short answer | |
| Jan 30, 2021 at 17:05 | history | edited | Aksakal | CC BY-SA 4.0 |
added 26 characters in body
|
| Jan 30, 2021 at 16:45 | comment | added | Richard Hardy | This is not in line with the linked definition of consistency. See also this answer and this thread that explain how consistency implies asymptotic unbiasedness. | |
| Jan 30, 2021 at 16:42 | history | rollback | Richard Hardy |
Rollback to Revision 1
|
|
| Jan 30, 2021 at 16:34 | history | edited | Richard Hardy | CC BY-SA 4.0 |
added 15 characters in body
|
| Jan 30, 2021 at 15:48 | comment | added | Aksakal | You can have an estimator that is consistent and asymptotically biased. It will converge to the wrong value steadily as sample increases. For instance $\hat\mu=e^{\bar\ln x}$ when x is log normal | |
| Jan 30, 2021 at 15:42 | comment | added | Richard Hardy | If it were asymptotically biased, it would not be consistent. What I am trying to get at is that unbiased is unnecessary and misleading in this context. | |
| Jan 30, 2021 at 15:31 | comment | added | Aksakal | If the sample variance was biased even asymptotically then normalizing would not yield standard normal. It would be normal but not variance 1. MLE variance is biased but not asymptotically. | |
| Jan 30, 2021 at 9:02 | comment | added | Richard Hardy | So if the sample variance were biased and consistent, you could not use it? (I would not think bias has much relevance in large samples.) You comment also raises another question: is normality really needed for the variance estimator to be unbiased? | |
| Jan 29, 2021 at 23:31 | comment | added | Aksakal | @RichardHardy under assumptions such as normal distribution in my example | |
| Jan 29, 2021 at 9:36 | comment | added | Richard Hardy | due to its being <...> unbiased. Is it so? | |
| Jan 29, 2021 at 1:29 | history | answered | Aksakal | CC BY-SA 4.0 |