The reduction of the average width of confidence bands for an unknown continuous distribution function

Abstract

In this article we introduce an algorithm that produces confidence bands with smaller average width than the previously considered bands, such as the Kolmogorov–Smirnov, Berk–Jones bands and so forth. These new bands are called quasi-minimum average width (MAW) bands. The average width of bands is defined by Xu et al. [Xu et al., 2007, A new confidence band for continuous distribution functions. submitted for publication.]. The maximum coverage of bands subject to an average width constraint is also considered. We employ MATLAB to develop programmes. The comparisons between the new bands and the other bands are then carried out, from which it can be seen that the new bands have some nice power properties in goodness-of-fit test. Based on some calculational evidences we have a speculation that the new bands are the bands with MAW.