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Saddlepoint approximations to studentized bootstrap distributions based onM-estimates

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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.

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Acknowledgement

The author expresses his deep gratitude to his PhD thesis supervisor A. C. Davison for his suggestions relating to this work, which was supported by a grant from the Swiss National Science Foundation.

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  1. Statoo Consulting, PO Box 107, 1015, Lausanne, Switzerland

    Diego Kuonen

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  1. Diego Kuonen
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Kuonen, D. Saddlepoint approximations to studentized bootstrap distributions based onM-estimates. Computational Statistics 20, 231–244 (2005). https://doi.org/10.1007/BF02789701

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