Mean location, the two sample problem Harrie Hendriks, Mathematics, Radboud University Nijmegen

Harrie Hendriks (May 25, 2012)

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The context will be the estimation of a parameter of a probability distribution, where the parameter lies in a differentiable manifold, more specifically in a submanifold of Euclidean space. The parameter could be a Frechet mean of a probability distribution on the submanifold itself, Frechet mean with respect to the Euclidean distance. We will give an account of the two-sample problem.

This talk is based on joint work with Zinoviy Landsman. Examples from the literature will be indicated. Downs considered the QRS loop in vectorcardiograms, characterized by a pair of orthogonal unit vectors in 3-space. The space of such pairs is the Stiefel manifold V32, and can be considered as submanifold of 6-dimensional Euclidean space. A more involved example, considered by Rivest et al., is the human ankle joint that exhibits two independent rotation axes of the foot. The directions of these axes are of importance.