# Math Help - MSE of uniform with order statistic estimators

1. ## MSE of uniform with order statistic estimators

Hi,

I have a an iid sample of $U(\theta_1, \theta_2)$ and have gotten the MLE to be
$\hat \theta_1 = X_{(1)}$ and $\hat \theta_2 = X_{(n)}$

I am looking to find the MSE for each of the MLE's. I'm getting stuck on the variance since it's the order statistic and not just the variance of a uniform variable? I'd appreciate any input sending me in the right direction...

Thank you!

2. Hello,

If I'm not confusing, you have no other choice than finding the pdf of X(1) and X(n), via the cdf (which is not too difficult to find).

3. ## MSE

Moo,

Thanks for the note - that does make sense to me.

(PS: Nein, dumm bin ich nicht! ;-) )

4. Originally Posted by Statistik
Hi,

I have a an iid sample of $U(\theta_1, \theta_2)$ and have gotten the MLE to be
$\hat \theta_1 = X_{(1)}$ and $\hat \theta_1 = X_{(1)}$

I am looking to find the MSE for each of the MLE's. I'm getting stuck on the variance since it's the order statistic and not just the variance of a uniform variable? I'd appreciate any input sending me in the right direction...

Thank you!

I assume you mean $\hat \theta_1 = X_{(1)}$ and $\hat \theta_2 = X_{(n)}$

5. ## correction

Matheagle,

You are absolutely right, thanks. I edited the above post to reflect the correction.

6. half way there, you still have an incorrect subscript

7. ## continued correction...

Argh - sorry... Fixing it now. (Hopefully, that's it - since you said 1/2 way and I made one correction, one more should get me there... ;-) )