## The Annals of Statistics

### On Differentiable Functionals

#### 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

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