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ON THE BOOTSTRAP AND TWO‐SAMPLE PROBLEMS
Author(s) -
Hall Peter,
Martin Michael
Publication year - 1988
Publication title -
australian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 0004-9581
DOI - 10.1111/j.1467-842x.1988.tb00474.x
Subject(s) - percentile , statistics , mathematics , confidence interval , sample size determination , sample (material) , constant (computer programming) , systematic error , computer science , physics , thermodynamics , programming language
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.