Robust estimation of the location of a vertical tangent in distribution. (English) Zbl 0862.62027

Summary: It is shown that the location of the set of \(m+1\) observations with minimal diameter, within local data, is a robust estimator of the location of a vertical tangent in a distribution function. The rate of consistency of these estimators is shown to be the same as that of asymptotically efficient estimators for the same model.
Robustness means (1) only properties of the distribution local to the vertical tangent play a role in the asymptotics, and (2) these asymptotics can be proven given approximate information about just two parameters, the shape and quantile of the vertical tangent.


62F12 Asymptotic properties of parametric estimators
62F35 Robustness and adaptive procedures (parametric inference)
62E20 Asymptotic distribution theory in statistics
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