Saddlepoint approximations to studentized bootstrap distributions based onM-estimates

Summary  Saddlepoint methods can provide extremely accurate approximations to resampling distributions. This article applies them to distributions of studentized bootstrap statistics based on robustM-estimates. As examples we consider the studentized versions of Huber’sM-estimate of location, of its initially MAD scaled version, and of Huber’s proposal 2. The studentized version of Huber’s proposal 2 seems to be a preferable measure of location. Remarks on implementation and related problems are given.