Timeline for Unbiased estimator for $\mu_1/\mu_2$
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
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| Aug 16, 2022 at 23:01 | vote | accept | RiXaTorAgu | ||
| Aug 14, 2022 at 18:00 | history | tweeted | twitter.com/StackStats/status/1558876114612789248 | ||
| Aug 14, 2022 at 16:09 | answer | added | whuber♦ | timeline score: 4 | |
| Aug 13, 2022 at 8:31 | comment | added | Sextus Empiricus | @whuber the references might not be so bad. For many practical cases the distribution of $X/Y$ might not need to be like a pathological distribution without moments (this happens when $Y$ is only approximately normal distributed and does not approach zero unlike the normal distribution by which it is approximated). In such practical cases an approximation with a normal distribution does not need to be so bad. | |
| Aug 12, 2022 at 18:39 | history | edited | RiXaTorAgu | CC BY-SA 4.0 |
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| Aug 12, 2022 at 14:11 | comment | added | RiXaTorAgu | @whuber I was trying to build a known distribution from the samples, like a Gamma or something like that but so far I haven't achieved anything... | |
| Aug 12, 2022 at 13:52 | history | edited | RiXaTorAgu | CC BY-SA 4.0 |
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| Aug 12, 2022 at 13:31 | comment | added | whuber♦ | @user2974951 Those references might lead readers to confuse the random variables $X_i/Y_i$ with the ratio of means $\mu_1/\mu_2.$ What the question seeks is an estimator $t_n(X_1,\ldots, Y_n)$ for which $E[t_n(X_1,\ldots,Y_n)]=\rho.$ What is relevant about your points is that it would be hopeless to construct $t_n$ out of ratios of the variables or of their sample means, suggesting an unbiased estimator does not exist. When we couple that observation with the idea of using a minimal sufficient statistic, which obviously is $(\bar X,\bar Y),$ we're well on the way to a (negative) solution. | |
| Aug 12, 2022 at 6:22 | comment | added | user2974951 | en.wikipedia.org/wiki/… | |
| Aug 12, 2022 at 6:21 | comment | added | user2974951 | Related Is the ratio distribution of two normally distributed variables ever normal? | |
| S Aug 12, 2022 at 5:26 | review | First questions | |||
| Aug 12, 2022 at 5:54 | |||||
| S Aug 12, 2022 at 5:26 | history | asked | RiXaTorAgu | CC BY-SA 4.0 |