# Set estimation from reflected Brownian motion

arXiv: https://arxiv.org/abs/1411.0433 · HTML: https://mlsanity.com/paper/1411.0433/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Nov 2014.

## Built on by (most cited first, 2 of 2)

- [GROS: A General Robust Aggregation Strategy](https://mlsanity.com/paper/2402.15442/) (2024)
- [Boundary Detection Algorithm Inspired by Locally Linear Embedding](https://mlsanity.com/paper/2406.18456/) (2024)

## Abstract (arXiv)

We study the problem of estimating a compact set Ssubset ℝd from a trajectory of a reflected Brownian motion in S with reflections on the boundary of S. We establish consistency and rates of convergence for various estimators of S and its boundary. This problem has relevant applications in ecology in estimating the home range of an animal based on tracking data. There are a variety of studies on the habitat of animals that employ the notion of home range. This paper offers theoretical foundations for a new methodology that, under fairly unrestrictive shape assumptions, allows one to find flexible regions close to reality. The theoretical findings are illustrated on simulated and real data examples.