The Geometry of Nonparametric Filament Estimation

Details The Geometry of Nonparametric Filament Estimation The Geometry of Nonparametric Filament Estimation

2010-03-25

arxiv.org/abs/1003.5536v2

Mathematics

Statistics Theory

substantial revision

Scientific paper

We consider the problem of estimating filamentary structure from planar point process data. We make some connections with computational geometry and we develop nonparametric methods for estimating the filaments. We show that, under weak conditions, the filaments have a simple geometric representation as the medial axis of the data distribution's support. Our methods convert an estimator of the support's boundary into an estimator of the filaments. We also find the rates of convergence of our estimators.

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