Set estimation from reflected Brownian motion

Alejandro Cholaquidis, Ricardo Fraiman, Gábor Lugosi, Beatriz Pateiro-López

Journal of the Royal Statistical Society: Series B (Statistical Methodology) · 2016 · Volume 78 · Issue 5

Abstract

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

Keywords

Home range estimation, Reflected Brownian motion, Set estimation

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