Nonparametic estimation of location and dispersion on Riemannian manifolds

By Rabi N. Bhattacharya, Vic Patrangenaru. 2002

85 citations recorded by the source corpus.

Subfields: Applied Mathematics, Geometry and Topology, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/81c1faef4268134029b760883cd52768a9beceee

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In Applied Mathematics

In Geometry and Topology

In Statistics and Probability

Citations in the corpus

Intrinsic Statistics on Riemannian Manifolds: Basic Tools for Geometric Measurements (2006, background): “In [37, 38], the authors focused on the asymptotic consistency properties of the extrinsic and intrinsic means and variances for large sample sizes, and were able to propose a central limit theorem for ﬂat manifolds.”
Efficient algorithms for inferences on Grassmann manifolds (2004, methodology): “(ii) Intrinsic statistics, where the Riemannian structure ofGn,k is used to define uniquely statistics of interest [11].”
Population Shape Regression from Random Design Data (2007, background): “The large sample properties of sample means on manifolds are developed in Bhattacharya and Patrangenaru (2002, 2003) .”
Nonparametric statistics on manifolds with applications to shape spaces (2008, background): “In the case of the intrinsic mean and variation, the usual support criterion (see, e.g., Le [24] and Bhattacharya and Patrangenaru [ 6 , 7, 8]) is significantly relaxed, thereby substantially enhancing the applicability of the tests.”
LARGE SAMPLE THEORY OF INTRINSIC AND EXTRINSIC SAMPLE MEANS ON MANIFOLDS—II (2003, methodology): “This is a continuation of our earlier work [ 7 , 8] where some general properties of extrinsic and intrinsic mean sets on general manifolds were derived, and the problem of consistency of the corresponding sample indices was explored.”
Non-parametric regression estimation on closed Riemannian manifolds (2006, background): “An intrinsic mean of a probability measure μ on a Riemannian manifold M is a minimizer of the energy functional 23 27 28 This statement holds whenever the bandwidth is small enough.”
Analysis of planar shapes using geodesic paths on shape spaces (2004, background): “There are at least two ways of dening a \mean" value for a random variable that takes values on S1. The rst denition, called extrinsic mean, involves embedding the manifold in a vector space, computing the Euclidean mean in that space, and then projecting it down to the manifold [ 1 , 27].”
Kernel density estimation on Riemannian manifolds (2005, methodology): “(10) This definition is used in Bhattacharya and Patrangenaru (2002, 2003) for instance, while in (Corcuera and Kendall, 1999; Oller and Corcuera, 1995), the authors mainly consider those points p ∈ M satisfying the criticality condition: ∫ Tp(M) uµ̃(du) = 0, (11) where µ̃ is a probability measure…”