  In the mean-median-mode triad of univariate centrality measures, the mode has
been overlooked for estimating the center of symmetry in continuous and
unimodal settings. This paper expands on the connection between kernel mode
estimators and M-estimators for location, bridging the gap between the
nonparametrics and robust statistics communities. The variance of modal
estimators is studied in terms of a bandwidth parameter, establishing
conditions for an optimal solution that outperforms the household sample mean.
A purely nonparametric approach is adopted, modeling heavy-tailedness through
regular variation. The results lead to an estimator proposal that includes a
novel one-parameter family of kernels with compact support, offering extra
robustness and efficiency. The effectiveness and versatility of the new method
are demonstrated in a real-world case study and a thorough simulation study,
comparing favorably to traditional and more competitive alternatives. Several
myths about the mode are clarified along the way, reopening the quest for
flexible and efficient nonparametric estimators.
