Breakdown bounds and expected test resistance

Abstract

In many estimation problems the highest possible breakdown point is 50% of the sample. However, this is not always the case. We give an upper bound for the breakdown point of equivariant estimators in the k-sample model. The two-sample model is also discussed and estimators that achieve the bounds are highlighted. The expected resistance, a new criterion for robust tests, is proposed. The expected resistance to rejection (or acceptance) is essentially the expected proportion of contamination necessary to move a test statistic from the acceptance (or rejection) region into the rejection (or acceptance) region. It averages the resistance of a test statistic over all possible samples under the null (or alternative) hypothesis. The expected resistances of the sign test are derived and the expected resistance to rejection of two-sample tests are simulated and reported.