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summary We present asymptotic theory for the bootstrap in two‐sample problems. If the samples are of sizes m and n , then our results show that one‐sided and two‐sided percentile‐ t confidence intervals have coverage error O(m ‐1 + n ‐1 ), and that symmetric two‐sided intervals have coverage error O(m ‐2 + n ‐1 ). Furthermore, coverage error of all percentile‐t intervals drops to O(m ‐2 + n ‐2 ) when the populations the Normal. This decrease in error is also evidenced in a simulation study, and indicates that percentile‐ t provides a respectable solution to the Behrens‐Fisher problem. In addition we derive an explicit formula for the acceleration constant needed to implement accelerated bias‐correction in two‐sample problems.
Hall et al. (Sun,) studied this question.