Set estimation from reflected Brownian motion

• 成果类型: Article
• 署名作者: Cholaquidis, Alejandro; Fraiman, Ricardo; Lugosi, Gabor; Pateiro-Lopez, Beatriz
• 署名单位: Universidad de la Republica, Uruguay; ICREA; Pompeu Fabra University; Universidade de Santiago de Compostela
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1111/rssb.12149
• 发表日期: 2016
• 页码: 1057-1078
• 关键词: STOCHASTIC DIFFERENTIAL-EQUATIONS; home-range; kernel methods; convex-hull; MOVEMENT; BOUNDARY; models; shape

摘要

We study the problem of estimating a compact set S subset of R-d 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 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.