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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
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