On Robust and Efficient Estimation of the Center of Symmetry

In this article, a class of estimators of the center of symmetry based on the empirical characteristic function is examined. In the spirit of the Hodges–Lehmann estimator, the resulting procedures are shown to be a function of the pairwise averages. The proposed procedures are also shown to have an equivalent representation as the minimizers of certain distances between two corresponding kernel density estimators. An alternative characterization of the Hodges–Lehmann estimator is established upon the use of a particularly simple choice of kernel.