Sufficient conditions for the Cramer-Rao inequality are formulated which do not impose any requirement on the estimator and which are independent of the choice of the densities. A hereditary property is proved for these conditions and the attainability of the lower bound is studied.
"On the Cramer-Rao Inequality." Ann. Statist. 5 (1) 197 - 205, January, 1977. https://doi.org/10.1214/aos/1176343754