On exactness and unbiasedness of confidence bands for a continuous distribution function

We define a class of confidence bands for distribution functions, named simple confidence bands. The class of bands includes the common step bands and continuous bands, some of which may perform better than the smoothed bands not belonging to the class, e.g., the kernel smoothed bands. It is shown t...

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Bibliographic Details
Published in:Science China. Mathematics 2010-10, Vol.53 (10), p.2665-2678
Main Authors: Ding, XiaoBo, Xu, XingZhong, Zhao, Shuran
Format: Article
Language:English
Subjects:
Applications of Mathematics
Mathematics
Mathematics and Statistics
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Summary:We define a class of confidence bands for distribution functions, named simple confidence bands. The class of bands includes the common step bands and continuous bands, some of which may perform better than the smoothed bands not belonging to the class, e.g., the kernel smoothed bands. It is shown that under some mild assumptions, the simple bands with exact coverage for continuous distribution functions are all step bands. The unbiasedness problem of the step bands is also investigated. It is proved that most of two-sided step bands are biased and one-sided step bands are unbiased.
ISSN:1674-7283
1869-1862
1862-2763
DOI:10.1007/s11425-010-4034-3