Glivenko-Cantelli lemma

Let X1,,Xn be iid as X with (unknown) distribution functionMathworldPlanetmath F. Let ω be the outcome and Fn(x,ω) be the empirical distribution function based on observations X1(ω),,Xn(ω). Then, as n,

sup-<x<|Fn(x,ω)-F(x)|0 a.s.,

where a.s. means almost surely.

Title Glivenko-Cantelli lemma
Canonical name GlivenkoCantelliLemma
Date of creation 2013-03-22 14:33:24
Last modified on 2013-03-22 14:33:24
Owner CWoo (3771)
Last modified by CWoo (3771)
Numerical id 4
Author CWoo (3771)
Entry type Theorem
Classification msc 62G20