MINIMAX PROPERTIES OF FRECHET MEANS OF DISCRETELY SAMPLED CURVES

• 成果类型: Article
• 署名作者: Bigot, Jeremie; Gendre, Xavier
• 署名单位: Universite de Toulouse; Institut Superieur de l'Aeronautique et de l'Espace (ISAE-SUPAERO); Universite de Toulouse; Universite Toulouse III - Paul Sabatier
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/13-AOS1104
• 发表日期: 2013
• 页码: 923-956
• 关键词: Manifolds; shape; CONVERGENCE; Consistency

摘要

We study the problem of estimating a mean pattern from a set of similar curves in the setting where the variability in the data is due to random geometric deformations and additive noise. We propose an estimator based on the notion of Frechet mean that is a generalization of the standard notion of averaging to non-Euclidean spaces. We derive a minimax rate for this estimation problem, and we show that our estimator achieves this optimal rate under the asymptotics where both the number of curves and the number of sampling points go to infinity.