User:Baccyak4H/pages/Influence Function

In statistics, an influence function is a property of a regression model quantifying the dependence of an estimated parameter of the model as a function of the data.

Definition
For a univariate distribution function F and a functional T which operates on distributions to return a parameter of the distribution, the influence function IF(x;F,T) is defined as

$$ \operatorname{IF}(x;F,T) = \lim_{\epsilon \downarrow 0} \frac{T[(1 - \epsilon) F + \epsilon\,\delta_{x}] - T(F)} {\epsilon}, $$

where &delta;x is the distribution function of a point mass at x.

External sources
Hoaglin, Mosteller & Tukey; Understanding Robust and Exploratory Data Analysis; John Wiley & Sons, 1983