Non-asymptotic Confidence Sets for Extrinsic Means on Spheres and Projective Spaces

Thomas Hotz; Florian Kelma

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arXiv · 1602.04117

Non-asymptotic Confidence Sets for Extrinsic Means on Spheres and Projective Spaces

Thomas Hotz·Florian Kelma

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Abstract

Confidence sets from i.i.d. data are constructed for the extrinsic mean of a probabilty measure P on spheres, real projective spaces, and complex projective spaces, as well as Grassmann manifolds, with the latter three embedded by the Veronese-Whitney embedding. When the data are sufficiently concentrated, these are projections of a ball around the corresponding Euclidean sample mean. Furthermore, these confidence sets are rate-optimal. The usefulness of this approach is illustrated for projective shape data.

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Thomas Hotz, Florian Kelma. 2016-02-12. Non-asymptotic Confidence Sets for Extrinsic Means on Spheres and Projective Spaces. https://arxiv.org/abs/1602.04117

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