High-order coverage of smoothed Bayesian bootstrap intervals for population quantiles
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Using fractional order statistics, we characterize the high-order frequentist coverage probability of smoothed and unsmoothed Bayesian bootstrap credible intervals for population quantiles. The original Rubin (1981) unsmoothed intervals have O(n-1/2) coverage error, whereas intervals based on the smoothed Bayesian bootstrap of Banks (1988) have much smaller O(n−3/2[log(n)]3) coverage error. No smoothing parameter is required. In special cases, the smoothed intervals are exact. Simulations illustrate our results.