The breakdown value is a popular measure of the robustness of an estimator against outlying observations. Roughly speaking, it indicates the smallest fraction of contaminants in a sample that causes the estimator to break down, that is, to take on values that are arbitrarily bad or meaningless. In this paper, we recall the definition of the finite sample as well as the asymptotic breakdown value of an estimator, and we give several examples of well-known estimators for location, scatter, and regression. We discuss the maximal attainable breakdown values and give an overview of high-breakdown estimators that attain this maximal bound. Finally, we refer to some issues in more complex models. Copyright © 2009 John Wiley & Sons, Inc.
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