Home range estimation under a restricted sampling scheme

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.