# MSE of uniform with order statistic estimators

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• Apr 17th 2010, 09:28 PM
Statistik
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!
• Apr 22nd 2010, 01:27 AM
Moo
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).
• Apr 22nd 2010, 07:50 PM
Statistik
MSE
Moo,

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

(PS: Nein, dumm bin ich nicht! ;-) )
• Apr 22nd 2010, 10:18 PM
matheagle
Quote:

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 $\hat \theta_2 = X_{(n)}$
• Apr 24th 2010, 09:19 PM
Statistik
correction
Matheagle,

You are absolutely right, thanks. I edited the above post to reflect the correction.
• Apr 24th 2010, 09:30 PM
matheagle
half way there, you still have an incorrect subscript
• Apr 24th 2010, 09:35 PM
Statistik
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... ;-) )