Improving Coverage Accuracy of Nonparametric Prediction Intervals

Research Report SRR01-001

Improving Coverage Accuracy of Nonparametric Prediction Intervals

Peter Hall and Andrew Rieck

Abstract: Methods are suggested for improving coverage of intervals for predicting future values of a random variable from a sampled distribution. It is shown that the properties of solutions to such problems may be quite unexpected. For example, the bootstrap and the jackknife perform very poorly when used to calibrate coverage, despite the jackknife estimator of true coverage being virtually unbiased. A version of the smoothed bootstrap can be employed for successful calibration, however. Interpolation among adjacent order statistics can also be an effective way of calibrating, although even there the results are unexpected. In particular, while coverage error can be reduced from O(n^-1) to orders O(n^-2) and O(n^-3) (where n denotes sample size) by interpolating among two and three order statistics, respectively, the next two orders of reduction require interpolation among five and eight order statistics, respectively.

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