Summary
We show that the percentile-t method, and one of the two percentile methods, have unusually good performance when employed to construct bootstrap confidence intervals in a regression setting. In the case of slope parameters, percentile-t produces two-sided intervals with coverage errorn -2, and one-sided intervals with coverage errorn -3/2, wheren is sample size. The errors are onlyn -1 in most other problems. One of the percentile methods produces critical points which are third-order correct for Efron's [11] relatively complex accelerated bias-corrected points.
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Hall, P. Unusual properties of bootstrap confidence intervals in regression problems. Probab. Th. Rel. Fields 81, 247–273 (1989). https://doi.org/10.1007/BF00319554
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DOI: https://doi.org/10.1007/BF00319554