Abstract
We compare extrinsic and intrinsic means for circular data with respect to criteria such as uniqueness, computational complexity, robustness, and asymptotic relative efficiency. Moreover, we construct universal, rate-optimal confidence sets for the extrinsic mean. We conclude that neither location estimator outperforms the other in general. However, due to its simplicity, greater robustness and the existence of universal, rate-optimal confidence sets for it, the extrinsic mean appears preferable to the intrinsic mean unless one knows in advance that the underlying distribution is unimodal.
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