Studentized bootstrap confidence intervals based on M-estimates

This article reviews and applies saddlepoint approximations to studentized confidence intervals based on robust M-estimates. The latter are known to be very accurate without needing standard theory assumptions. As examples, the classical studentized statistic, the studentized versions of Huber's M-estimate of location, of its initially MAD scaled version and of Huber's proposal 2 are considered. The aim is to know whether the studentized statistics yield robust confidence intervals with coverages close to nominal, with short intervals. The results of an extensive simulation study and the recommendations for practical use given in this article may fill gaps in the current literature and stimulate further discussion and research.