The analysis of animal movement has gained attention recently. New continuous-time models and statistical methods have been developed to estimate some sets related to their movements, such as the home-range and the core-area among others, when the information of the trajectory is provided by a GPS. Because data transfer costs and GPS battery life are practical constraints in ecological studies, the experimental designer must make critical sampling decisions in order to maximize information. To capture fine-scale motion, long-term behavior must be sacrificed, and vice versa. To overcome this limitation, we introduce the on--off sampling scheme, where the GPS is alternately on and off. This scheme is already used in practice but with insufficient statistical theoretical support. We prove the consistency of home-range estimators with an underlying reflected diffusion model under this sampling method (in terms of the Hausdorff distance). The same rate of convergence is achieved as in the case where the GPS is always on for the whole experiment. This is illustrated by a simulation study and real data. We also provide estimators of the stationary distribution, its level sets (which give estimators of the core area), and the drift function.

翻译：动物运动分析近期受到广泛关注。当通过GPS获取轨迹信息时，已开发出新的连续时间模型和统计方法来估计与运动相关的集合，如家域和核心区域等。由于数据传输成本和GPS电池寿命是生态研究中的实际限制因素，实验设计者必须做出关键采样决策以最大化信息获取。为捕捉精细尺度运动，需牺牲长期行为，反之亦然。为克服这一限制，我们引入开关采样方案（GPS交替开启与关闭）。该方案虽已在实践中使用，但缺乏足够的统计理论支持。我们证明在此采样方法下（以豪斯多夫距离衡量），基于反射扩散模型的家域估计量具有一致性，且收敛速率与整个实验期间GPS始终开启的情况相同。这一结论通过模拟研究和真实数据得到验证。我们还提供了平稳分布、其水平集（可给出核心区域估计量）以及漂移函数的估计方法。