We study functional central limit theorems for persistent Betti numbers obtained from networks defined on a Poisson point process. The limit is formed in large volumes of cylindrical shape stretching only in one dimension. The results cover a directed sublevel-filtration for stabilizing networks and the Čech and Vietoris–Rips complex on the random geometric graph. The presented functional central limit theorems open the door to a variety of statistical applications in topological data analysis and we consider goodness-of-fit tests in a simulation study.
CITATION STYLE
Krebs, J., & Hirsch, C. (2022). Functional central limit theorems for persistent Betti numbers on cylindrical networks. Scandinavian Journal of Statistics, 49(1), 427–454. https://doi.org/10.1111/sjos.12524
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