A counterexample to a conjecture concerning the Hall-Wellner band

Abstract

Hall and Wellner proposed a natural extension of the Kolmogorov-Smirnov simultaneous confidence band for survival curve using the Kaplan-Meier estimator. They and Gill conjectured that the confidence band holds for all t up to the last observed failure time. A counterexample is given herein, showing that this may not always be true.