P. Saavedra Nieves, R. M. Crujeiras
Set estimation is focused on the reconstruction of a set (or the estimation of any of its features) from a random sample of points. Target sets to be estimated appear in different contexts, but from a distribution-based perspective, level set estimation is a problem of interest. Actually, this theory is also linked to clustering methods: Hartigan (1975) defines the number of population clusters as the number of connected components of density level sets. This topic has received some attention in the literature specially for densities supported on an Euclidean space. However, this clustering approach can be easily extended to more general settings such as the circle or the sphere. In this work, we derive some methodology for estimating the number of directional clusters as the number of connected components of directional level sets. An extensive simulation study shows the performance of the proposed estimator for densities supported on the unit circle and the sphere.
Keywords: Clustering, connected components, density level sets, directional data
Scheduled
GT18 Non-parametric statistics II. Nonparametric inference for density and distribution
June 9, 2022 12:00 PM
A15
