An Anscombe type robust regression statistic. (English) Zbl 0900.62166
Summary: A new robust regression estimator is proposed. Its use involves sampling of elemental set in a schema very similar to Rousseeuw’s least median of squares. Since the construction of such a statistics is done on the basis of residuals from regression, the problem reduces to parameter estimation in a one-dimensional sample, in the face of outliers. Our proposal relies on the work done by Anscombe; it uses the ideas of insurance premium and protection applied to outlier identification, with the addition of Rosner’s backwards elimination. This new estimator may represent a modest improvement over methods like the LMS, in that it appears to be able to solve marginal cases resistant so far, requiring the extraction of fewer elemental sets in order to reach a reasonable likelihood of success. The proposed method, however, is not uniformly preferable to the LMS and it should complement the latter rather than replace it.
MSC:
| 62F35 | Robustness and adaptive procedures (parametric inference) |
| 62J99 | Linear inference, regression |
Keywords:
Regression outlier; Elemental set/regression; Least median of squares; Small residuals; Anscombe type statistic; Breakdown point; Exact fit propertyReferences:
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