The effect of Monte Carlo approximation on coverage error of double-bootstrap confidence intervals
Journal of the Royal Statistical Society: Series B (Statistical Methodology) · 1999 · Volume 61 · Issue 2
Abstract
A double-bootstrap confidence interval must usually be approximated by a Monte Carlo simulation, consisting of two nested levels of bootstrap sampling. We provide an analysis of the coverage accuracy of the interval which takes account of both the inherent bootstrapandMonte Carlo errors. The analysis shows that, by a suitable choice of the number of resamples drawn at the inner level of bootstrap sampling, we can reduce the order of coverage error. We consider also the effects of performing a finite Monte Carlo simulation on the mean length and variability of length of two-sided intervals. An adaptive procedure is presented for the choice of the number of inner level resamples. The effectiveness of the procedure is illustrated through a small simulation study.
Keywords
Bootstrap, Coverage error, Double bootstrap, Monte Carlo approximation, Percentile method, Resample, Sampling error, Stimulation
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