Home-range estimation under a restricted sample scheme

AbstractNew continuous-time models and statistical methods have been developed to estimate some sets related to animal movement, 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, the experimental designer must make critical sampling decisions to maximise information. 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. 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 and the drift function.Keywords: Home-range estimationreflected Brownian motion with driftstationarity distributionlevel set estimation2010 Mathematics Subject Classifications: 62M2062G2060J70 AcknowledgmentsWe thanks Dr. Stephen Blake, of the Max Planck Institute for Ornithology, for facilitating access to the data set that was used in this paper. The data that support the findings of this study are openly available in Movebank at https://www.movebank.org/cms/webapp?gwt_fragment=page=studies,path=study1818825, reference number 1818825.We thanks the editor and three referee's for their constructive comments which improves significantly the present version of the manuscript.Disclosure statementNo potential conflict of interest was reported by the author(s).Additional informationFundingThis work was supported by grants ANII (Agencia Nacional de Investigación e Innovación) [grant numbers POSNAC20191157608, FCE120191156054].