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The Edgeworth expansion for U-statistics established by Bickel, Götze, and van Zwet is combined with the von Mises expansion to derive an Edgeworth expansion with remainder for the Kaplan-Meier (KM) estimator. We show that the Edgeworth expansion of the KM estimator has the form:
, where Φ is the standard normal distribution function, φ is the standard normal density function, and
is the asymptotic third cumulant of the KM estimator.
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