H. González-Vázquez, B. Pateiro-López, A. Rodríguez-Casal
Manifold estimation allows for a non-linear and non-parametric dimension reduction when working with data in an euclidean space that are actually supported on (or close to) a lower dimension manifold, providing a better understanding on their underlying structure. In the particular case when the manifold is a curve, the problem is known as filament estimation. The aim of this work is to propose a new filament estimator, called the Euclidean Distance Transform (EDT) estimator with r-convex hull, which builds upon the EDT estimator introduced by Genovese et al. (2012), and incorporates a shape restriction that generalizes convexity, known as r-convexity. In a certain model with compact noise, our estimator achieves the optimal rate in minimax sense of convergence in Hausdorff distance, up to logarithmic factor, when the ambient space is the plane. Additionally, we illustrate its application in estimating tree stem cross-sections in forest inventory.
Palabras clave: filament estimation, manifold learning, set estimation, minimax estimator, r-convex hull, forest inventory
Programado
Estimación no paramétrica
12 de junio de 2025 19:00
Sala de prensa (MR 13)