User:Baccyak4H/pages/Influence Function
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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.
[edit] 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},](../../../../math/9/7/e/97e30554bab1032f5b695b0ecfecb09c.png)
where δx is the distribution function of a point mass at x.
[edit] See also
Hoaglin, Mosteller & Tukey; Understanding Robust and Exploratory Data Analysis; John Wiley & Sons, 1983
