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

Rabi Bhattacharya, Vic Patrangenaru

Research output: Contribution to journalArticle

189 Scopus citations

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 1 2003

Keywords

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

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Fingerprint Dive into the research topics of 'Large sample theory of intrinsic and extrinsic sample means on manifolds. I'. Together they form a unique fingerprint.

  • Cite this