  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.
