Improving coverage accuracy of nonparametric prediction intervals |
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Authors: | Peter Hall & Andrew Rieck |
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Institution: | Australian National University, Canberra, Australia |
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Abstract: | Methods are suggested for improving the coverage accuracy of intervals for predicting future values of a random variable drawn from a sampled distribution. It is shown that 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, although the jackknife estimator of the true coverage is 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, whereas the coverage error can be reduced from O ( n -1) to orders O ( n -2) and O ( n -3) (where n denotes the 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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Keywords: | Bootstrap Calibration Density estimation Interpolation Jackknife Monte Carlo methods Order statistic Quantile Smoothed bootstrap |
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