It is shown that under certain conditions, the maximum likelihood and the minimum variance unbiased estimators of a positive integral power of the natural parameter in an exponential family have the same asymptotic distribution.
"Asymptotic Equivalence of Two Estimators for an Exponential Family." Ann. Statist. 1 (5) 973 - 980, September, 1973. https://doi.org/10.1214/aos/1176342519