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Given a sample of size n from a distribution P_, one wants to estimate a functional () of the (typically infinite-dimensional) parameter. Lower bounds on the performance of estimators can be based on the concept of a differentiable functional P_ (). In this paper we relate a suitable definition of differentiable functional to differentiability of dP^1/2_ and (). Moreover, we show that regular estimability of a functional implies its differentiability.
Aad van der Vaart (Fri,) studied this question.