# Clarification on the difference between the UMVUE and the estimator that achieves CRLB

I am confused about this. Are they the same? There are some problems in which I am asked to find the Uniformly Minimum Variance Unbiased Estimator (UMVUE) first and then check if it achieves the CRLB. Yet from what I've read, I understand that an unbiased estimator that achieves CRLB is UMVUE. Thanks.

• @user164144 Yes, if the unbiased estimator is a function of a complete sufficient statistic, then it is the UMVUE. This is the Lehmann-Scheffe theorem. In particular, let $T$ be a complete sufficient statistic and $S$ an unbiased estimator. Then $E[S | T]$ gives the UMVUE. – Flowsnake Jul 6 '17 at 1:03