
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...

$\displaystyle X_{(n)}$ 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 $\displaystyle {n+1\over n}X_{(n)}$ since $\displaystyle E(X_{(n)})={na\over n+1}$.