Importance Sampling for Bootstrap Confidence Intervals
Abstract The use of importance-sampling methods to substantially reduce the amount of resampling necessary for the construction of nonparametric bootstrap confidence intervals is investigated. The classical importance-sampling method of Hammersley and Handscomb (1964) is modified to apply to the estimation of quantiles. Based on this method, a resampling procedure is introduced that recenters the bootstrap distribution of a robust estimator of location to produce estimated confidence limits that are much more accurate (for a given amount of resampling) than those obtained by the usual bootstrap method (Efron 1982). The required recentering is accomplished with a suitable “exponential tilting” similar to that used in another connection by Field and Hampel (1982). This importance-sampling procedure is used to produce bootstrap confidence intervals for location based on a class of estimators that includes symmetric M estimators. These interval estimates are asymptotically optimal in a certain sense. Simulati...