Confidence bands from censored samples

Several types of asymptotic confidence bands have been proposed in the literature when the data are randomly censored on the right. Introducing new classes of bands, we place the old bands and their relationship to one another within a comprehensive theory of bands. A thorough analysis yields narrower bands and two kinds of modifications which are asymptotically distribution- and censor-free. One of these is useful when the interval on which the bands are constructed is predetermined and the width of the bands is random; the other, when there is a predetermined bound on the width and the interval is random. We illustrate our bands on the Szeged pacemaker data. These methods also provide a general modification of the Kolmogorov band in the uncensored case.