REGULAR REDESCENDING RANK ESTIMATES

A study is made of some unusual location estimates first proposed in 1 977 by J. S. Maritz, M. Wu, and R. G. Staudte, Jr., who established so me strong robustness properties of these estimates, such as redescendi ng influence functions and, in some cases, full efficiency at the Cauc hy model. It is further shown here that the estimates, called M-W-S es timates, are derivable from a rank-based scheme founded on convex func tions and hence are regular, are unique, and have associated tests and confidence intervals. The tests belong to a family of signed-rank-typ e tests, and their distributions have nice combinatorial properties. I t is not the case, therefore, that a redescending influence function n eed imply all the computational irregularities possessed by redescendi ng M estimates. In addition, M-W-S estimates are shown to have breakdo wn point of .5, a very strong robustness property.