  As estimators of location parameters, univariate trimmed means are well known
for their robustness and efficiency. They can serve as robust alternatives to
the sample mean while possessing high efficiencies at normal as well as
heavy-tailed models. This paper introduces multidimensional trimmed means based
on projection depth induced regions. Robustness of these depth trimmed means is
investigated in terms of the influence function and finite sample breakdown
point. The influence function captures the local robustness whereas the
breakdown point measures the global robustness of estimators. It is found that
the projection depth trimmed means are highly robust locally as well as
globally. Asymptotics of the depth trimmed means are investigated via those of
the directional radius of the depth induced regions. The strong consistency,
asymptotic representation and limiting distribution of the depth trimmed means
are obtained. Relative to the mean and other leading competitors, the depth
trimmed means are highly efficient at normal or symmetric models and
overwhelmingly more efficient when these models are contaminated. Simulation
studies confirm the validity of the asymptotic efficiency results at finite
samples.
