| Abstract: | The breakdown point of an estimator is the smallest fraction of contamination that can force the value of the estimator beyond the boundary of the parameter space. It is well known that the highest possible breakdown point, under equivariance restrictions, is 50% of the sample. However, this upper bound is not always attainable. We give an example of an estimation problem in which the highest possible attainable breakdown point is much less than 50% of the sample. For hypothesis testing, we discuss the resistance of a test and propose new definitions of resistance. The maximum resistance to rejection (acceptance) is the smallest fraction of contamination necessary to force a test to reject (fail to reject) regardless of the original sample. We derive the maximum resistances of the t-test and sign test in the one-sample problem and of the t-test and Mood test in the two-sample problem. We briefly discuss another measure known as the expected resistance. |
