A NEW CONFIDENCE BAND FOR CONTINUOUS CUMULATIVE DISTRIBUTION FUNCTIONS

Summary We consider confidence bands for continuous distribution functions. Following a review of the literature we find that previously considered confidence bands, which have exact coverage, are all step‐functions jumping only at the sample points. We find that the step‐function bands can be const...

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Bibliographic Details
Published in:Australian & New Zealand journal of statistics 2009-09, Vol.51 (3), p.305-318
Main Authors: Xu, Xingzhong, Ding, Xiaobo, Zhao, Shuran
Format: Article
Language:English
Subjects:
average width
Berk-Jones
confidence bands
exact coverage
Kolmogorov-Smirnov
Noé's recursion
power
reversed Berk-Jones
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Summary:Summary We consider confidence bands for continuous distribution functions. Following a review of the literature we find that previously considered confidence bands, which have exact coverage, are all step‐functions jumping only at the sample points. We find that the step‐function bands can be constructed through rectangular tolerance regions for an ordered sample from the uniform distribution R(0, 1). We then construct a set of new bands. Two criteria for assessing confidence bands are presented. One is the power criterion, and the other is the average‐width criterion that we propose. Numerical comparisons between our new bands and the old bands are carried out, and show that our new bands perform much better than the old ones.
ISSN:1369-1473
1467-842X
DOI:10.1111/j.1467-842X.2009.00546.x