# Extent of occurrence reconstruction using a new data-driven support estimator

## TL;DR

This paper introduces a new data-driven method for estimating the probability support of a distribution, using an r-convex set estimator with an algorithm to determine the shape parameter from data, applicable to ecological data.

## Contribution

The paper presents a stochastic algorithm to estimate the shape parameter r for r-convex support sets, enabling flexible and accurate support reconstruction from data.

## Key findings

- Achieves convergence rates similar to convex hull estimators for convex sets.
- Provides a practical algorithm for estimating the shape parameter r.
- Demonstrates application to ecological data for invasive species.

## Abstract

Given a random sample of points from some unknown distribution, we propose a new data-driven method for estimating its probability support S. Under the mild assumption that S is r-convex, the smallest r-convex set which contains the sample points is the natural estimator. The main problem for using this estimator in practice is that r is an unknown geometric characteristic of the set S. A stochastic algorithm is proposed for determining an optimal estimate of r from the data under mild regularity assumptions on the density function. The resulting data-driven reconstruction of S attains the same convergence rates as the convex hull for estimating convex sets, but under a much more flexible smoothness shape condition. The new support estimator will be used for reconstructing the extent of occurrence of an assemblage of invasive plant species in the Azores archipelago.