Large sample theory of intrinsic and extrinsic sample means on manifolds. I

Rabindra N Bhattacharya, Vic Patrangenaru

Research output: Contribution to journalArticle

180 Citations (Scopus)

Abstract

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 Q̂ n. Asymptotic distributions of extrinsic sample means are derived. Explicit computations of these indices of Q̂ n and their asymptotic dispersions are carried out for distributions on the sphere S d (directional spaces), real projective space ℝP N-1 (axial spaces) and ℂP k-2 (planar shape spaces).

Original languageEnglish (US)
Pages (from-to)1-29
Number of pages29
JournalAnnals of Statistics
Volume31
Issue number1
DOIs
StatePublished - Feb 2003
Externally publishedYes

Fingerprint

Large Sample Theory
Sample mean
Shape Space
Projective Space
Asymptotic distribution
Probability Measure
Riemannian Manifold
Uniqueness
Sufficient Conditions
Intrinsic

Keywords

  • Consistency
  • Equivariant embedding
  • Extrinsic mean
  • Fréchet mean
  • Intrinsic mean
  • Mean planar shape

ASJC Scopus subject areas

  • Mathematics(all)
  • Statistics and Probability

Cite this

Large sample theory of intrinsic and extrinsic sample means on manifolds. I. / Bhattacharya, Rabindra N; Patrangenaru, Vic.

In: Annals of Statistics, Vol. 31, No. 1, 02.2003, p. 1-29.

Research output: Contribution to journalArticle

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