I am wondering whether Dvoretzky–Kiefer–Wolfowitz inequality holds for discrete distributions? Any comments or references would be greatly appreciated.
2026-03-29 17:24:38.1774805078
Dvoretzky–Kiefer–Wolfowitz inequality holds for discrete distributions?
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Yes, the Dvoretzky–Kiefer–Wolfowitz (DKW) inequality holds unchanged for discrete distributions.
See, for example, Comment 2(iii) of Massart (1990): "inequalities (1.4) and (1.5) remain valid when F is not continuous." In particular, Inequality (1.5) is the two-sided DKW inequality.