On estimating the perimeter using the alpha-shape

DOI10.1214/16-AIHP747MaRDI QIDQ2403212

Ery Arias-Castro, Alberto Rodríguez Casal

Publication date: 15 September 2017

Published in: Annales de l'Institut Henri Poincaré. Probabilités et Statistiques (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1507.00065

zbMATH Keywords

\(\alpha\)-shapesets with positive reachperimeter estimation\(r\)-convex hullrolling condition

Mathematics Subject Classification ID

Density estimation (62G07) Nonparametric estimation (62G05) Geometric probability and stochastic geometry (60D05)

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Minimax Euclidean separation rates for testing convex hypotheses in \(\mathbb{R}^{d}\) ⋮ Polynomial volume estimation and its applications ⋮ A data-adaptive method for estimating density level sets under shape conditions ⋮ Estimation of surface area ⋮ Adaptive density estimation on bounded domains under mixing conditions ⋮ Quantifying Different Modeling Frameworks Using Topological Data Analysis: A Case Study with Zebrafish Patterns ⋮ Nonparametric estimation of surface integrals on level sets ⋮ Minimax Estimation of the Volume of a Set Under the Rolling Ball Condition

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