Robustness properties for a simple class of rank estimates

Robustness properties of a family of rank estimates to compete with trimmed means and other robust estimates for the one sample location problem are investigated. In particular, the influence curve and breakdown point are developed, as well as their finite sample equivalents, the sensitivity curve and tolerance. The estimates are formulated from a one sample rank test rather than the customary two sample rank test approach. In addition, a functional is implicitly defined for the asymptotic version of the estimate. Computational problems are considered and a simple iterative procedure for finding the estimate is given.