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Abstract:
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In recent years, analyzing data on manifolds has received increased attention in many statistical applications as a means to provide accurate inference based on usage of underlying geometry of the object space. Numerous robust methods have been extensively studied on Euclidean spaces, whereas much less attention has been paid to manifold data. In this paper we introduce a robust extrinsic framework for conducting manifold valued data analysis. First, by extending the notion of the geometric median in an Euclidean space to the embedded manifold case, we propose a new robust location parameter so-called extrinsic median. A robust regression method is also developed by incorporating local polynomial regression methods and the extrinsic median. We present the Weiszfeld's algorithm for computing these proposed manifold valued statistics. The promising performance of our approach against existing methods is illustrated through simulation study.
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