This paper presents a uniform estimator for a finite-dimensional parameter in the semiparametric Weibull mixture model. The rates achieved by the estimator hold uniformly over shrinking sequences of models much more general than traditional sequences that are required to satisfy a Hellinger differentiable property. We show that these rates are optimal in a class of identified models constrained by a moment condition on the nonparametric mixing distribution.
"Uniform rates of estimation in the semiparametric Weibull mixture model." Ann. Statist. 24 (4) 1572 - 1585, August 1996. https://doi.org/10.1214/aos/1032298285