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Math Help - MSE of uniform with order statistic estimators

  1. #1
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    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!
    Last edited by Statistik; April 24th 2010 at 08:35 PM.
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  2. #2
    Moo
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    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).
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  3. #3
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    MSE

    Moo,

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

    (PS: Nein, dumm bin ich nicht! ;-) )
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  4. #4
    MHF Contributor matheagle's Avatar
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    Quote Originally Posted by Statistik View Post
    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)}
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  5. #5
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    correction

    Matheagle,

    You are absolutely right, thanks. I edited the above post to reflect the correction.
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  6. #6
    MHF Contributor matheagle's Avatar
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    half way there, you still have an incorrect subscript
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  7. #7
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    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... ;-) )
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