Breakdown point

Summary

The breakdown point of an estimator is the smallest fraction of the data that can ruin the estimate. Ruin means that replacing this fraction by arbitrary values can carry the estimate arbitrarily far. It measures the global robustness of an estimator against gross outliers. The sample mean has breakdown point $1/n$, which tends to $0$. The median has breakdown point close to $1/2$, the largest possible value for equivariant estimators of location.