期刊
TECHNOMETRICS
卷 53, 期 1, 页码 44-53出版社
AMER STATISTICAL ASSOC
DOI: 10.1198/TECH.2010.09114
关键词
MM estimate; S estimate; Shrinking
资金
- University of Buenos Aires
- CONICET [PID 5505]
- ANPCyT, Argentina [PICT 00899]
Ridge regression, being based on the minimization of a quadratic loss function, is sensitive to outliers. Current proposals for robust ridge-regression estimators are sensitive to bad leverage observations, cannot be employed when the number of predictors p is larger than the number of observations n, and have a low robustness when the ratio pin is large. In this article a ridge-regression estimate based on repeated M estimation (MM estimation) is proposed. It is a penalized regression MM estimator, in which the quadratic loss is replaced by an average of rho(r(i)/(sigma) over cap), where r(i) are the residuals and (sigma) over cap the residual scale from an initial estimator, which is a penalized S estimator; and rho is a bounded function. The MM estimator can be computed for p > n and is robust for large p/n. A fast algorithm is proposed. The advantages of the proposed approach over its competitors are demonstrated through both simulated and real data. Supplemental materials are available online.
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