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This article develops nonparametric inference procedures for estimation andtesting problems for means on manifolds. A central limit theorem for Frechetsample means is derived leading to an asymptotic distribution theory ofintrinsic sample means on Riemannian manifolds. Central limit theorems are alsoobtained for extrinsic sample means w.r.t. an arbitrary embedding of adifferentiable manifold in a Euclidean space. Bootstrap methods particularlysuitable for these problems are presented. Applications are given todistributions on the sphere S^d (directional spaces), real projective spaceRP^{N-1} (axial spaces), complex projective space CP^{k-2} (planar shapespaces) w.r.t. Veronese-Whitney embeddings and a three-dimensional shape space\Sigma_3^4.

Large sample theory of intrinsic and extrinsic sample means on manifolds—II