Testing goodness of fit for point processes via topological data analysis

DOI10.1214/20-EJS1683zbMath1440.62409arXiv1906.07608OpenAlexW3008725893MaRDI QIDQ2180054

Christian Hirsch, Anne Marie Svane, Nicolas Chenavier, Christophe Ange Napoléon Biscio

Publication date: 13 May 2020

Published in: Electronic Journal of Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1906.07608

zbMATH Keywords

central limit theorempoint processesgoodness-of-fit teststopological data analysispersistent Betti number

Mathematics Subject Classification ID

Nonparametric hypothesis testing (62G10) Geometric probability and stochastic geometry (60D05) Measures of association (correlation, canonical correlation, etc.) (62H20) Generalized (extraordinary) homology and cohomology theories in algebraic topology (55N20) Functional limit theorems; invariance principles (60F17) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55) Topological data analysis (62R40)

Related Items (9)

Extremal lifetimes of persistent cycles ⋮ A functional central limit theorem for the empirical Ripley's \(K\)-function ⋮ Topology-based goodness-of-fit tests for sliced spatial data ⋮ Persistent homology based goodness-of-fit tests for spatial tessellations ⋮ Limit theory of sparse random geometric graphs in high dimensions ⋮ Bootstrapping persistent Betti numbers and other stabilizing statistics ⋮ Topology-driven goodness-of-fit tests in arbitrary dimensions ⋮ On approximation theorems for the Euler characteristic with applications to the bootstrap ⋮ Functional limit theorems for the euler characteristic process in the critical regime

Uses Software

• spatstat
• TDA
• GET

Cites Work

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