Abstract: This paper concerns the use of simulation procedures to construct second-order accurate confidence limits having coverage error of order o(n-1). An explicit formula for the analytical adjustment required in Efron's (1987) BCa percentile method is derived, automatic percentile methods that do not require analytical adjustments are proposed, and variance-stabilizing transformations designed to improve the performance of the bootstrap-t method are given. The automatic percentile methods and variance-stabilizing transformations involve a least favorable family construction of Stein (1956), which is related to orthogonal parameters. Connections with approximate limits obtained using profile likelihood methods are also discussed.
Key words and phrases: Approximate confidence limit, bootstrap-t, conditional inference, least favorable family, orthogonal parameters, percentile method, second-order accuracy, signed root adjusted likelihood ratio statistic, variance-stabilizing transformation.