  Recently, there has been a growing need in analyzing data on manifolds owing
to their important role in diverse fields of science and engineering. In the
literature of manifold-valued data analysis up till now, however, only a few
works have been carried out concerning the robustness of estimation against
noises, outliers, and other sources of perturbations. In this regard, we
introduce a novel extrinsic framework for analyzing manifold valued data in a
robust manner. First, by extending the notion of the geometric median, we
propose a new robust location parameter on manifolds, so-called the extrinsic
median. A robust extrinsic regression method is also developed by incorporating
the conditional extrinsic median into the classical local polynomial regression
method. We present the Weiszfeld's algorithm for implementing the proposed
methods. The promising performance of our approach against existing methods is
illustrated through simulation studies.
