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Dvoretzky-Kiefer-Wolfowitz Inequality

From Wikipedia, the free encyclopedia

Let $X i$ be i.i.d. from some distribution with distribution function $F$ . Let $\hat F_n$ be the associated empirical distribution functions. The Dvoretzky-Kiefer-Wolfowitz (DKW) Inequality gives $Pr (sup_t | \hat F_n(t) - F(t)| > \epsilon) \leq 2e^{-2n\epsilon^2}$ .

This strengthens the Glivenko-Cantelli Theorem by giving rates of convergence.

[edit] References

The references in this article would be clearer with a different and/or consistent style of citation, footnoting or external linking.

All of Statistics. Larry Wasserman.

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