REVIEW 3 cited by
A short proof of the Dvoretzky--Kiefer--Wolfowitz--Massart inequality
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
read the original abstract
The Dvoretzky--Kiefer--Wolfowitz--Massart inequality gives a sub-Gaussian tail bound on the supremum norm distance between the empirical distribution function of a random sample and its population counterpart. We provide a short proof of a result that improves the existing bound in two respects. First, our one-sided bound holds without any restrictions on the failure probability, thereby verifying a conjecture of Birnbaum and McCarty (1958). Second, it is local in the sense that it holds uniformly over sub-intervals of the real line with an error rate that adapts to the behaviour of the population distribution function on the interval.
Forward citations
Cited by 3 Pith papers
-
A data-dependent DKW inequality for regenerative Markov chains
Establishes an empirical concentration inequality for the empirical CDF of a functional on regenerative Markov chains, with data-dependent leading term and lower-order convergence bound.
-
An Elementary Proof of the Dvoretzky--Kiefer--Wolfowitz--Massart Inequality
A discrete-martingale plus Sion-minimax argument proves P(sup(ˆF_n−F)>ε)≤exp(−2nε²) for every ε>0, recovering the classical DKW–Massart bound.
-
Coverage correlation: detecting singular dependencies between random variables
The coverage correlation estimates how much of a joint distribution is concentrated on a singular set, claiming values near 0 for independence and 1 for fully singular dependence.
Discussion (0). Continue with ORCID to comment.