  Advances in computing power enable more widespread use of the mode, which is
a natural measure of central tendency since, as the most probable value, it is
not influenced by the tails in the distribution. The properties of the
half-sample mode, which is a simple and fast estimator of the mode of a
continuous distribution, are studied. The half-sample mode is less sensitive to
outliers than most other estimators of location, including many other low-bias
estimators of the mode. Its breakdown point is one half, equal to that of the
median. However, because of its finite rejection point, the half-sample mode is
much less sensitive to outliers that are all either greater or less than the
other values of the sample. This is confirmed by applying the mode estimator
and the median to samples drawn from normal, lognormal, and Pareto
distributions contaminated by outliers. It is also shown that the half-sample
mode, in combination with a robust scale estimator, is a highly robust starting
point for iterative robust location estimators such as Huber's M-estimator. The
half-sample mode can easily be generalized to modal intervals containing more
or less than half of the sample. An application of such an estimator to the
finding of collision points in high-energy proton-proton interactions is
presented.
