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SUMMARY A survey of bootstrap procedures for constructing confidence regions is given. In particular, several distinct bootstrap methods are considered, with emphasis on the mathematical correctness of these procedures. The percentile, bias‐corrected percentile and accelerated bias‐corrected percentile methods, developed by Efron, are reviewed in both parametric and nonparametric situations. A procedure related to the accelerated bias‐corrected method, which avoids explicit calculation of the analytical corrections required in Efron's method, is also introduced. In the context of a functional approach for the construction of confidence regions, the bootstrap is motivated as a method to estimate the distributions of approximate pivots. Finally, iterative bootstrap methods are discussed as means to improve coverage accuracy.

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