# How to find the asymptotic distribution of an estimator given the mean and variance of an estimator

I understand that the Delta Method can be used to find asymptotic distribution of estimators.

I have a MLE Estimator with

$$E[\hat\Theta] = \frac{n\Theta_0}{n+1}$$

$$Var[\hat\Theta] = \frac{\Theta^2_0}{n(n+2)}$$

How can I find the asymptotic distribution of this estimator?

• Jan 22, 2020 at 8:10
• Is this the only available information? You can only say $E[\hat\theta]\to \theta_0$ and $Var[\hat\theta]\to 0$, so $\hat\theta$ converges in probability (and hence in distribution) to $\theta_0$. This of course gives a degenerate asymptotic distribution. Jan 22, 2020 at 14:35
• Thank you for your response. The problem provides this info as the mean and variance of MLE of a uniform distribution over [0,$\Theta$]. The problem then asks for an asymptotic distribution for such a MLE estimator. Jan 22, 2020 at 20:33
• In that case see stats.stackexchange.com/q/130447/119261 for the non-degenerate asymptotic distribution. Jan 23, 2020 at 13:32
• Nov 2, 2020 at 20:23