High-order Coverage of Smoothed Bayesian Bootstrap Intervals for Population Quantiles

We characterize the high-order coverage accuracy of smoothed and unsmoothed Bayesian bootstrap confidence intervals for population quantiles. Although original (Rubin 1981) have same O(n−1/2) error as standard empirical bootstrap, Banks (1988) has much smaller O(n−3/2[log(n)]3) is exact in special cases, without requiring any smoothing parameter. It automatically removes an term order 1/n that other approaches need to explicitly correct for. This motivates further study more complex settings models.