Timeline for Can I use the delta method with a function that depends on n to approximate the distribution of a function of the sum of iid random variables?
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
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| Aug 18, 2021 at 11:32 | vote | accept | DM-97 | ||
| Aug 18, 2021 at 10:58 | comment | added | DM-97 | Thanks. Yeah, it seems surprising at first that $\log(\bar{X_n})$ and $\log(X^n)$ have the same variance, but I guess that actually makes a lot of sense, since $\log(\bar{X_n})=\log(\frac{1}{n}X^n)=\log(X^n)-\log(n)$. | |
| Aug 16, 2021 at 23:48 | answer | added | Geoffrey Johnson | timeline score: 1 | |
| Aug 16, 2021 at 23:31 | comment | added | Geoffrey Johnson | Yes, this looks correct to me. Interestingly, I also get $\frac{\sigma^2}{n\mu^2}$ as the asymptotic variance for $\text{log}(\bar{X})$. I suppose the best way to double check all of this is through simulation. I'll give it a try... | |
| Aug 16, 2021 at 22:01 | history | edited | DM-97 | CC BY-SA 4.0 |
fixed a mistake; changed notation to avoid confusion
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| Aug 16, 2021 at 21:37 | history | asked | DM-97 | CC BY-SA 4.0 |