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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

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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  • 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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    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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