Robust Statistics: The Approach Based on Influence Functions

Hampel, Ronchetti, Rousseeuw & Stahel (1986) — influence functions

Result

for a statistical functional $T$ at $F$, the asymptotic variance is $V(T,F)=\int \mathrm{IF}(x;T,F)^2\,dF(x)$.

Use

O6.2's $\sigma^2=E[\psi^2]$ is this formula; O6's selftest checks the closed-form $\psi$ against Gateaux finite differences, which is the definition of the influence function.

Verification

Chapter 2 begins p. 78 (primary record); $V(T,F)=\int\mathrm{IF}^2dF$ is cited to p. 85 within §2.1 (secondary); equation numbers unresolved (audit 5 Sep 2026).