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On (in)consistency of M-estimators under contamination

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  • Jens Klooster
  • Bent Nielsen

Abstract

We consider robust location-scale estimators under contamination. We show that commonly used robust estimators such as the median and the Huber estimator are inconsistent under asymmetric contamination, while the Tukey estimator is consistent. In order to make nuisance parameter free inference based on the Tukey estimator a consistent scale estimator is required. However, standard robust scale estimators such as the interquartile range and the median absolute deviation are inconsistent under contamination.

Suggested Citation

  • Jens Klooster & Bent Nielsen, 2025. "On (in)consistency of M-estimators under contamination," Papers 2502.09145, arXiv.org.
    • Handle: RePEc:arx:papers:2502.09145
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    References listed on IDEAS

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    1. Johansen, Søren & Nielsen, Bent, 2019. "Boundedness Of M-Estimators For Linear Regression In Time Series," Econometric Theory, Cambridge University Press, vol. 35(3), pages 653-683, June.
    2. Horowitz, Joel L & Manski, Charles F, 1995. "Identification and Robustness with Contaminated and Corrupted Data," Econometrica, Econometric Society, vol. 63(2), pages 281-302, March.
    3. 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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