Umvue

WeeG · #1 $Old$ June 6th, 2009, 04:40 AM

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...

matheagle · #2 $Old$ June 6th, 2009, 08:39 AM

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