Open Access
February 2014 A Parametric Framework for the Comparison of Methods of Very Robust Regression
Marco Riani, Anthony C. Atkinson, Domenico Perrotta
Statist. Sci. 29(1): 128-143 (February 2014). DOI: 10.1214/13-STS437


There are several methods for obtaining very robust estimates of regression parameters that asymptotically resist 50% of outliers in the data. Differences in the behaviour of these algorithms depend on the distance between the regression data and the outliers. We introduce a parameter $\lambda$ that defines a parametric path in the space of models and enables us to study, in a systematic way, the properties of estimators as the groups of data move from being far apart to close together. We examine, as a function of $\lambda$, the variance and squared bias of five estimators and we also consider their power when used in the detection of outliers. This systematic approach provides tools for gaining knowledge and better understanding of the properties of robust estimators.


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Marco Riani. Anthony C. Atkinson. Domenico Perrotta. "A Parametric Framework for the Comparison of Methods of Very Robust Regression." Statist. Sci. 29 (1) 128 - 143, February 2014.


Published: February 2014
First available in Project Euclid: 9 May 2014

zbMATH: 1332.62245
MathSciNet: MR3201859
Digital Object Identifier: 10.1214/13-STS437

Keywords: Distance of outliers , Forward search , least trimmed squares , MM estimate , multiple outliers , overlap index , point contamination , regression diagnostics

Rights: Copyright © 2014 Institute of Mathematical Statistics

Vol.29 • No. 1 • February 2014
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