  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.
