Robustness to Outliers of Bounded-Error Estimators and Consequences on Experiment Design
If proper precautions are not taken, bounded-error estimators are not robust to outliers, i.e., to data points where the actual error is larger than assumed when specifying the error bounds. The outlier minimal number estimator (OMNE) has been designed to overcome this difficulty and has proved on various examples to be particularly insensitive to outliers. This chapter is devoted to a theoretical study of its robustness. The notion of breakdown point, introduced to quantify the robustness of point estimators, is extended to set-estimators. When the model output is linear in the parameters, OMNE is shown to possess the highest achievable breakdown point. A bound on the bias due to outliers is established and used to define a new policy for optimal experimental design aimed at providing a higher protection against outliers than conventional D-optimal design.
KeywordsDesign Matrix Full Rank Design Policy Breakdown Point Regular Data
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