ROBUST ESTIMATION OF THE LOCATION OF A VERTICAL TANGENT IN DISTRIBUTION

It is shown that the location of the set of m + 1 observations with mi nimal diameter, within local data, is a robust estimator of the locati on of a vertical tangent in a distribution function. The rate of consi stency of these estimators is shown to be the same as that of asymptot ically efficient estimators for the same model. Robustness means (1) o nly properties of the distribution local to the vertical tangent play a role in the asymptotics, and (2) these asymptotics can be proven giv en approximate information about just two parameters, the shape and qu antile of the vertical tangent.