Timeline for Prove the consistency of estimator
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 27, 2016 at 14:01 | vote | accept | Paul | ||
| Aug 27, 2016 at 13:58 | comment | added | Greenparker | Good. You did make a mistake though I think. It is written that $\theta$ is the rate parameter. Thus $\sum t_i \sim \Gamma(n, \theta)$ where $\theta$ is the rate parameter. For the rate parameter, $1/\sum t_i \sim IG(n, \theta)$, not $\theta^{-1}$. See my answer here. | |
| Aug 27, 2016 at 13:53 | comment | added | Paul | Hi, I try to put everything together. If $\sum t_i \sim \Gamma(n,\theta)$ then $\frac{1}{\sum t_i}\sim IG(n,\theta^{-1})$. Now, the variance of $IG$ should be $\mathbb{Var}(IG(n,\theta^{-1}))=\frac{\theta^{-2}}{(n-1)^2(n-2)}$ so $\lim_{n \to \infty}n^2\frac{\theta^{-2}}{(n-1)^2(n-2)}=0$ and this prove the consistency of $\hat \theta$. | |
| Aug 26, 2016 at 17:50 | history | answered | Greenparker | CC BY-SA 3.0 |