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Maximum deviation curves for location estimators.

By Christophe Croux

Abstract

The maximum deviation curve of an estimator describes how an estimate can change (in the worst case) when you replace m out of n ''good'' observations to arbitrary positions. This function will be computed for some robust univariate location estimators. A lower bound for this curve is derived, and it is shown that this bound can be attained Trimmed means will always be close to this lower bound. When more than one third of the observations is contaminated, the median also gets to the lower bound. Finally, it is shown that a high breakdown point leads to a relatively large maximum deviation in the presence of small amounts of contaminants. The maximum deviation curve approach is based on the finite sample behavior of the estimators and makes no distributional assumptions.bias curve; breakdown point; location estimator; maximum deviation; robustness; sensitivity; regression;

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