Bootstrap Confidence Intervals

Abstract : We describe the various techniques that were proposed for constructing non-parametric confidence intervals using the bootstrap. These include bootstrap pivotal intervals, percentile and bias-corrected percentile intervals, and non-parametric titling intervals. These methods are small sample improvements over the usual + or - standard deviation intervals. We discuss them in detail, outlining underlying assumptions in each case. We show how the non- parametric titling interval can be viewed as an extension of a bootstrap pivotal interval, and suggest a number of generalizations. Finally, the various intervals are compared in a small simulation study.