Using linear interpolation to reduce the order of the coverage error of nonparametric prediction intervals based on right-censored data

We prove a general result showing that a simple linear interpolation between adjacent random variables reduces the coverage error of nonparametric prediction intervals for a future observation from the same underlying distribution function from O(n(-1)) to O(n(-2)). To illustrate the result we show that it can be applied to various scenarios of right censored data including Type-II censored samples, pooled Type-II censored data, and progressively Type-II censored order statistics. We further illustrate the result by simulations indicating that the desired level of significance is almost attained for moderate sample sizes. (C) 2014 Elsevier Inc. All rights reserved.