## On differentiable functionals.(English)Zbl 0732.62035

Author’s abstract: Given a sample of size n from a distribution $$P_{\lambda}$$, one wants to estimate a functional $$\psi$$ ($$\lambda$$) of the (typically infinite-dimensional) parameter $$\lambda$$. Lower bounds on the performance of estimators can be based on the concept of a differentiable functional $$P_{\lambda}\to \psi (\lambda)$$. We relate a suitable definition of differentiable functional to differentiability of $$\lambda \to dP_{\lambda}^{1/2}$$ and $$\lambda \to \psi (\lambda)$$. Moreover, we show that regular estimability of a functional implies its differentiability.

### MSC:

 62G07 Density estimation 62G20 Asymptotic properties of nonparametric inference
Full Text: