The Annals of Statistics

A counterexample to a conjecture concerning the Hall-Wellner band

Kani Chen and Zhiliang Ying

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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.

Article information

Source
Ann. Statist., Volume 24, Number 2 (1996), 641-646.

Dates
First available in Project Euclid: 24 September 2002

Permanent link to this document
https://projecteuclid.org/euclid.aos/1032894456

Digital Object Identifier
doi:10.1214/aos/1032894456

Mathematical Reviews number (MathSciNet)
MR1394979

Zentralblatt MATH identifier
0859.62046

Subjects
Primary: 62E20: Asymptotic distribution theory
Secondary: 62G30: Order statistics; empirical distribution functions

Keywords
Censored survival data Kolmogorov-Smirnov statistic Brownian bridge Doob's transformation confidence band tightness weak convergence

Citation

Chen, Kani; Ying, Zhiliang. A counterexample to a conjecture concerning the Hall-Wellner band. Ann. Statist. 24 (1996), no. 2, 641--646. doi:10.1214/aos/1032894456. https://projecteuclid.org/euclid.aos/1032894456


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References

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  • CLEAR WATER BAY HILL CENTER, BUSCH CAMPUS
  • KOWLOON, HONG KONG PISCATAWAY, NEW JERSEY 08855