文章基本信息

标题：On the consistency of Fréchet means in deformable models for curve and image analysis
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作者：Jérémie Bigot ; Benjamin Charlier
期刊名称：Electronic Journal of Statistics
印刷版ISSN：1935-7524
出版年度：2011
卷号：5
页码：1054-1089
DOI：10.1214/11-EJS633
语种：English
出版社：Institute of Mathematical Statistics
摘要：A new class of statistical deformable models is introduced to study high-dimensional curves or images. In addition to the standard measurement error term, these deformable models include an extra error term modeling the individual variations in intensity around a mean pattern. It is shown that an appropriate tool for statistical inference in such models is the notion of sample Fréchet means, which leads to estimators of the deformation parameters and the mean pattern. The main contribution of this paper is to study how the behavior of these estimators depends on the number n of design points and the number J of observed curves (or images). Numerical experiments are given to illustrate the finite sample performances of the procedure.