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.