The notion of best asymptotically normal estimates--BAN estimates for short--was introduced by Neyman  in the multinomial case. Applications have been made in biological problems, notably in bio-assay , , . Generalizations of Neyman's work have been made by Barankin and Gurland , Chiang  and Ferguson . The usual theory of BAN estimates requires differentiability of the estimates, and imposes rather strong conditions on certain functions given in advance (the functions $\zeta$ and $\Sigma$ of Section 3). In this note a different definition of BAN estimates is made which does not require differentiability, at the same time relaxing the conditions on $\zeta$ and $\Sigma,$ whereas in essence all important theorems in the theory of BAN estimates are retained.
"On the Theory of Ban Estimates." Ann. Math. Statist. 30 (1) 185 - 191, March, 1959. https://doi.org/10.1214/aoms/1177706373