arXiv 13 Feb 2025 · Mathematics — Statistics Theory
arXiv:2502.09145 · PDF · DOI · OpenAlex · Extracted main text
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.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Huber, P. J (1984) Finite sample breakdown of M-and P-estimators | 1.000 | 7 | 4 | 100% |
| 2 | Donoho, D. L. and Huber, P. J (1983) The notion of breakdown point | 0.928 | 4 | 4 | 100% |
| 3 | Huber, P. J. and Ronchetti, E. M (2009) Robust Statistics | 0.928 | 4 | 3 | 100% |
| 4 | Berenguer-Rico, V., Johansen, S., and Nielsen, B (2023) A model where the Least Trimmed Squares estimator is maximum likelihood self | 0.874 | 8 | 2 | 100% |
| 5 | Berenguer-Rico, V. and Nielsen, B (2023) Least trim\-med squares asymptotics: Nuisance parameter free asymptotics self | 0.843 | 4 | 3 | 75% |
| 6 | Rousseeuw, P. J. and Leroy, A. M (1987) Robust Regression and Outlier Detection | 0.811 | 4 | 2 | 100% |
| 7 | Huber, P. J (1964) Robust estimation of a location parameter | 0.811 | 4 | 2 | 100% |
| 8 | Maronna, R. A., Martin, R. D., and Yohai, V. J (2006) Robust Statistics: Theory and Methods | 0.737 | 3 | 2 | 100% |
| 9 | Hampel, F. R (1971) A general qualitative definition of robustness | 0.737 | 3 | 2 | 100% |
| 10 | Yu, C. and Yao, W (2017) Robust linear regression: A review and comparison | 0.737 | 3 | 2 | 100% |
Showing the top 10 of 25 scored citations.