Qualms about Bootstrap Confidence Intervals

The percentile method and bias-corrected percentile method of Efron (1981, 1982) are discussed. When these methods are used to construct nonparametric confidence intervals for the variance of a normal distribution, the coverage probabilities are substantially below the nominal level for small to moderate samples. This is due to the inapplicability of assumptions underlying the methods. These assumptions are difficult or impossible to check in the complicated situations for which the bootstrap is intended. Therefore, bootstrap confidence intervals should be used with caution in complex problems.