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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.
Definition
editFor 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
![{\displaystyle \operatorname {IF} (x;F,T)=\lim _{\epsilon \downarrow 0}{\frac {T[(1-\epsilon )F+\epsilon \,\delta _{x}]-T(F)}{\epsilon }},}](https://wikimedia.org/api/rest_v1/media/math/render/svg/072ac039558975dd2c334bfebd84fddfcdca2845)
where δx is the distribution function of a point mass at x.
External sources
editHoaglin, Mosteller & Tukey; Understanding Robust and Exploratory Data Analysis; John Wiley & Sons, 1983