Sufficient conditions are given for the uniqueness of intrinsic and extrinsic means as measures of location of probability measures Q on Riemannian manifolds. It is shown that, when uniquely defined, these are estimated consistently by the corresponding indices of the empirical $\hat Q_n$. Asymptotic distributions of extrinsic sample means are derived. Explicit computations of these indices of $\hat Q_n$ and their asymptotic dispersions are carried out for distributions on the sphere $S^d$ (directional spaces), real projective space $\mathbb{R}P^{N-1}$ (axial
spaces) and $\mathbb{C} P^{k-2}$ (planar shape spaces).
Publié le : 2003-02-14
Classification:
Fréchet mean,
intrinsic mean,
extrinsic mean,
consistency,
equivariant embedding,
mean planar shape,
62H11,
62H10
@article{1046294456,
author = {Bhattacharya, Rabi and Patrangenaru, Vic},
title = {Large sample theory of intrinsic and extrinsic sample means on manifolds},
journal = {Ann. Statist.},
volume = {31},
number = {1},
year = {2003},
pages = { 1-29},
language = {en},
url = {http://dml.mathdoc.fr/item/1046294456}
}
Bhattacharya, Rabi; Patrangenaru, Vic. Large sample theory of intrinsic and extrinsic sample means on manifolds. Ann. Statist., Tome 31 (2003) no. 1, pp. 1-29. http://gdmltest.u-ga.fr/item/1046294456/