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Math Help - Umvue

  1. #1
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    Umvue

    Hello,

    Can someone please show me how to find a UMVUE to the parameter "a" when X1,...Xn ~ U(0,a), using the Lehman Scheffe theorem ?
    ( I do know what need to be done, finding an unbiased estimator which depends on a sufficient and complete statistic, but how ? )

    Actually, my biggest problem is showing that X(n) is complete...
    Last edited by WeeG; June 6th 2009 at 03:51 AM.
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  2. #2
    MHF Contributor matheagle's Avatar
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    X_{(n)} is suff for a, by the factorization theorem, it's also the MLE for a.

    Next, find it's density where f(x)=1/a and F(x)=x/a, for 0<x<a.

    The answer is {n+1\over n}X_{(n)} since E(X_{(n)})={na\over n+1}.
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