Interpolated Nonparametric Prediction Intervals and Confidence Intervals

Abstract

In several important statistical problems, prediction intervals and confidence intervals can be constructed with coverage levels which are known precisely but cannot be rendered equal to predetermined levels such as 0.95. One solution to this difficulty is to interpolate between such intervals. We show that simple linear interpolation reduces the order of coverage error, but that higher orders of interpolation produce no further improvement. The error is reduced by a factor n -1 for prediction intervals and n -1/2 for confidence intervals, where n denotes sample size. In the case of confidence intervals for quantiles, linear interpolation provides particularly accurate intervals which err on the side of conservatism