Journal
ANNALS OF APPLIED STATISTICS
Volume 14, Issue 1, Pages 409-432Publisher
INST MATHEMATICAL STATISTICS
DOI: 10.1214/19-AOAS1311
Keywords
Activity space; global positioning systems (GPS); human mobility; kernel density estimation; space-time geography; topological data analysis
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Funding
- National Science Foundation [DMS/MPS-1737746]
- National Institutes of Health [U01-AG016976]
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Activity spaces are fundamental to the assessment of individuals' dynamic exposure to social and environmental risk factors associated with multiple spatial contexts that are visited during activities of daily living. In this paper we survey existing approaches for measuring the geometry, size and structure of activity spaces, based on GPS data, and explain their limitations. We propose addressing these shortcomings through a nonparametric approach called density ranking and also through three summary curves: the mass-volume curve, the Betti number curve and the persistence curve. We introduce a novel mixture model for human activity spaces and study its asymptotic properties. We prove that the kernel density estimator, which at the present time, is one of the most widespread methods for measuring activity spaces, is not a stable estimator of their structure. We illustrate the practical value of our methods with a simulation study and with a recently collected GPS dataset that comprises the locations visited by 10 individuals over a six months period.
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