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High Breakdown-Point and High Efficiency Robust Estimates for Regression
Open accessAbstract
A class of robust estimates for the linear model is introduced. These estimates, called MM-estimates, have simultaneously the following properties: (i) they are highly efficient when the errors have a normal distribution and (ii) their breakdown-point is 0.5. The MM-estimates are defined by a three-stage procedure. In the first stage an initial regression estimate is computed which is consistent robust and with high breakdown-point but not necessarily efficient. In the second stage an M-estimate of the errors scale is computed using residuals based on the initial estimate. Finally, in the third stage an M-estimate of the regression parameters based on a proper redescending psi-function is computed. Consistency and asymptotical normality of the MM-estimates assuming random carriers are proved. A convergent iterative numerical algorithm is given. Finally, the asymptotic biases under contamination of optimal bounded influence estimates and MM-estimates are compared.
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Metadata
- Authors
- Yohai, V. J.
- Venue
- The Annals of Statistics
- Publisher
- Institute of Mathematical Statistics
- Published
- 1987-06-01
- Volume
- 15
- Issue
- 2
- ISSN
- 0090-5364 (ISSN-L)
- OpenAlex
- W2011627547
- Cited by
- 1,644
- References
- 0
- FWCI
- 5.68
- Type
- journal article
- Language
- en
- Open access
- bronze
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- Yohai, V. J. (1987). High Breakdown-Point and High Efficiency Robust Estimates for Regression. The Annals of Statistics. https://doi.org/10.1214/aos/1176350366
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