Estimation of the envelope of a point set with loose boundaries

Abstract Given a point set in R 2, its envelope is defined as a contour line of the density of points with a given proportion of the points excluded. Three methods are presented and compared to estimate the envelope: one is based on Voronoi tessellation, the second on a nonparametric density estimation, and the third approach is parametric. The proposed techniques are applied to detect the faster growing trees in tree growth data.