I am tasked with determining if a particular parameter can be estimated efficiently.
Given that an efficient estimator is an unbiased estimator which achieves the Cramer-Rao lower-bound, is the only way to answer this question by first finding the UMVUE, calculating its variance, and then comparing its variance to the reciprocal of the Fisher information in the sample? Sounds like a whole lot of calculation, not that it should be too difficult, but I'm wondering if there's a shortcut.