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


  • Chen, Zhiqiang
  • E. Tyler, David


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.

Suggested Citation

  • Chen, Zhiqiang & E. Tyler, David, 2004. "On the finite sample breakdown points of redescending M-estimates of location," Statistics & Probability Letters, Elsevier, vol. 69(3), pages 233-242, September.
  • Handle: RePEc:eee:stapro:v:69:y:2004:i:3:p:233-242

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    References listed on IDEAS

    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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