Confidence intervals for prediction intervals

When working with a single random variable, the simplest and most obvious approach when estimating a 1 - γ prediction interval, is to estimate the γ/2 and 1 - γ/2 quantiles. The paper compares the small-sample properties of several methods aimed at estimating an interval that contains the 1 - γ prediction interval with probability 1 - α. In effect, the goal is to compute a 1 - α confidence interval for the true 1 - γ prediction interval. The only successful method when the sample size is small is based in part on an adaptive kernel estimate of the underlying density. Some simulation results are reported on how an extension to non-parametric regression performs, based on a so-called running interval smoother.