Timeline for Proving an Estimator of the sample variance to be MVUE
Current License: CC BY-SA 4.0
16 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 22 at 8:26 | vote | accept | Subhasis Biswas | ||
| Apr 22 at 2:18 | answer | added | Thomas Lumley | timeline score: 2 | |
| Apr 21 at 15:46 | comment | added | jbowman | Distributional assumptions might have been presented in previous questions; this seems likely (to me) to be one of a series of questions, rather than a standalone. | |
| Apr 21 at 14:45 | comment | added | whuber♦ | The question is phrased in a general way, so please do not assume normality. The preceding comments do not offer a counterexample because any conclusion arising from a more restrictive assumption (such as Poisson or Normal or whatever) does not logically imply the assertion is false. | |
| Apr 21 at 12:22 | comment | added | Subhasis Biswas | @Henry It acts as a counterexample, right? If so, then normality should be assumed, I guess. Then I'll have to check out the threads that solve the problem by assuming $X$ is from $N(\mu,\sigma^2)$, where $\mu$ is not known. | |
| Apr 21 at 12:20 | comment | added | Subhasis Biswas | @User1865345 In the original question, it was not mentioned, so I couldn't presume that $X$ follows some normal distribution. However, looks like Henry has produced a counterexample. | |
| Apr 21 at 11:53 | comment | added | Henry | For example, if $X$ follows a Poisson distribution, you might find $\bar X$ is an unbiased estimator of the variance (as well as of the mean) and has a smaller variance. | |
| Apr 21 at 11:41 | comment | added | User1865345 | Was the distribution mentioned or not? | |
| Apr 21 at 10:51 | comment | added | Subhasis Biswas | @User1865345 I couldn't find a direct proof of the fact that it's the minimum variance. I can prove the rest of the stuff myself, i.e computing the variance itself. Any help regarding pointing to a source would be appreciated. | |
| Apr 21 at 10:36 | comment | added | User1865345 | Also, you can add how the other threads couldn't help Or what aspect you didn't understand. Otherwise it would likely be closed as a duplicate. | |
| Apr 21 at 10:31 | history | edited | User1865345 | CC BY-SA 4.0 |
added 15 characters in body; edited tags
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| Apr 21 at 10:29 | comment | added | User1865345 | Okay. Thanks for your update. | |
| Apr 21 at 10:28 | comment | added | Subhasis Biswas | @User1865345 I tried going through the relevant threads, but the answers do not seem to be exactly what I want (or they're usually beyond my current level of understanding). That's why I decided to make a fresh question. | |
| Apr 21 at 10:24 | comment | added | User1865345 | Hello Subhasis. Welcome here. Have you checked through the relevant posts here? As common as this question is, there should be some thread(s) that could be helpful to you. Have you checked any? | |
| S Apr 21 at 10:03 | review | First questions | |||
| Apr 21 at 17:39 | |||||
| S Apr 21 at 10:03 | history | asked | Subhasis Biswas | CC BY-SA 4.0 |