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On the finite sample breakdown points of redescending M-estimates of location

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  • Chen, Zhiqiang
  • E. Tyler, David
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    Abstract

    The finite sample breakdown points of scale equivariate redescending M-estimates of location are studied. In particular, a simple lower bound for the finite sample breakdown point of redescending M-estimates of location is given whenever the M-estimate of location is defined using the median absolute deviation about the median (MAD) as a scaling term. This lower bound is close to 0.49 for many common cases and depends on the configuration of the "good" data only through breakdown point of the MAD.

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    File URL: http://www.sciencedirect.com/science/article/B6V1D-4CSXKFD-6/2/d58ad7e8833d5a7ab3f2b8742db7c9e5
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    Bibliographic Info

    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 69 (2004)
    Issue (Month): 3 (September)
    Pages: 233-242

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    Handle: RePEc:eee:stapro:v:69:y:2004:i:3:p:233-242

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    Related research

    Keywords: Breakdown point MAD Redescending M-estimates;

    References

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    1. He, Xuming, et al, 1990. "Tail Behavior of Regression Estimators and Their Breakdown Points," Econometrica, Econometric Society, vol. 58(5), pages 1195-1214, September.
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    Cited by:
    1. Yonggang Hu & Yong Wang & Yi Wu & Qiang Li & Chenping Hou, 2011. "Generalized Mahalanobis depth in the reproducing kernel Hilbert space," Statistical Papers, Springer, vol. 52(3), pages 511-522, August.
    2. Hampel, Frank & Hennig, Christian & Ronchetti, Elvezio, 2011. "A smoothing principle for the Huber and other location M-estimators," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 324-337, January.

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