The Annals of Statistics

On Differentiable Functionals

Aad Van Der Vaart

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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.

Article information

Source
Ann. Statist., Volume 19, Number 1 (1991), 178-204.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176347976

Digital Object Identifier
doi:10.1214/aos/1176347976

Mathematical Reviews number (MathSciNet)
MR1091845

Zentralblatt MATH identifier
0732.62035

JSTOR
links.jstor.org

Subjects
Primary: 62G20: Asymptotic properties
Secondary: 62G05: Estimation

Keywords
Convolution theorem asymptotic efficiency semi-parametric model information operator efficient information mixture model censoring truncation

Citation

Vaart, Aad Van Der. On Differentiable Functionals. Ann. Statist. 19 (1991), no. 1, 178--204. doi:10.1214/aos/1176347976. https://projecteuclid.org/euclid.aos/1176347976


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