Timeline for What is the limiting distribution of $\sqrt{n}(\bar{X}_n-p)-\sqrt{n}(\bar{Y}_n-q)$?
Current License: CC BY-SA 4.0
9 events
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| Feb 4, 2022 at 14:28 | history | edited | Eli | CC BY-SA 4.0 |
fixed mismatched brackets '{', clarified how to estimate the covariance matrix with the delta method
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| Feb 4, 2022 at 13:19 | comment | added | kjetil b halvorsen♦ | @Bob: Please do not ask new questions in a comment, but as a new Question! | |
| Feb 4, 2022 at 8:44 | comment | added | Scortchi♦ | @Bob: Try to solve it the same way, & post a new question if you should get stuck at some point. | |
| Feb 4, 2022 at 4:08 | comment | added | Eli | Yes to your first question, but I wasn’t thinking of it that way though. The sample mean is maximum likelihood estimate of a $p$ in a $Binom(n, p)$ so you know it’s consistent. | |
| Feb 3, 2022 at 23:21 | vote | accept | Hermi | ||
| Feb 3, 2022 at 23:21 | comment | added | Hermi | Thanks! For the consistent estimate part, can I say that since $\bar{X}_n\to p$ and $\bar{Y}_n\to q$ in probability? This implies $\bar{X}_n$ and $\bar{Y}_n$ are consistent estimator. Then plug it into $f(p,q)$ to get the consistent estimator? | |
| Feb 3, 2022 at 20:55 | history | edited | Eli | CC BY-SA 4.0 |
clarified that p and q cannot be 0
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| Feb 3, 2022 at 20:12 | history | edited | Eli | CC BY-SA 4.0 |
improved formatting
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| Feb 3, 2022 at 20:07 | history | answered | Eli | CC BY-SA 4.0 |