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March, 1991 On Differentiable Functionals
Aad Van Der Vaart
Ann. Statist. 19(1): 178-204 (March, 1991). DOI: 10.1214/aos/1176347976

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 $P_\lambda \rightarrow \psi(\lambda)$. In this paper we relate a suitable definition of differentiable functional to differentiability of $\alpha \rightarrow dP^{1/2}_\lambda$ and $\lambda \rightarrow \psi(\lambda)$. Moreover, we show that regular estimability of a functional implies its differentiability.

Citation

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Aad Van Der Vaart. "On Differentiable Functionals." Ann. Statist. 19 (1) 178 - 204, March, 1991. https://doi.org/10.1214/aos/1176347976

Information

Published: March, 1991
First available in Project Euclid: 12 April 2007

zbMATH: 0732.62035
MathSciNet: MR1091845
Digital Object Identifier: 10.1214/aos/1176347976

Subjects:
Primary: 62G20
Secondary: 62G05

Rights: Copyright © 1991 Institute of Mathematical Statistics

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Vol.19 • No. 1 • March, 1991
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