how to find the UMVUE estimator of $\displaystyle \theta$?
{$\displaystyle {X_i} $i=1,2,3,...,n}, i.i.d from $\displaystyle U(\theta-1,\theta
+1)$
and the minimum sufficient statistics for$\displaystyle \theta$ is $\displaystyle X_(1),X_(n)$?
Hello,
We studied in class the estimators $\displaystyle \delta_\alpha=\alpha X_{(1)}+(1-\alpha)X_{(n)}$ and concluded that $\displaystyle \delta_{1/2}$ is the UMVUE among the $\displaystyle \delta_{\alpha}$.
But if I remember what the teacher said, it's a pain to find the UMVUE among all the unbiased estimators...
Hope this helps