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2020 Testing goodness of fit for point processes via topological data analysis
Christophe A. N. Biscio, Nicolas Chenavier, Christian Hirsch, Anne Marie Svane
Electron. J. Statist. 14(1): 1024-1074 (2020). DOI: 10.1214/20-EJS1683


We introduce tests for the goodness of fit of point patterns via methods from topological data analysis. More precisely, the persistent Betti numbers give rise to a bivariate functional summary statistic for observed point patterns that is asymptotically Gaussian in large observation windows. We analyze the power of tests derived from this statistic on simulated point patterns and compare its performance with global envelope tests. Finally, we apply the tests to a point pattern from an application context in neuroscience. As the main methodological contribution, we derive sufficient conditions for a functional central limit theorem on bounded persistent Betti numbers of point processes with exponential decay of correlations.


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Christophe A. N. Biscio. Nicolas Chenavier. Christian Hirsch. Anne Marie Svane. "Testing goodness of fit for point processes via topological data analysis." Electron. J. Statist. 14 (1) 1024 - 1074, 2020.


Received: 1 June 2019; Published: 2020
First available in Project Euclid: 24 February 2020

zbMATH: 07200224
MathSciNet: MR4067816
Digital Object Identifier: 10.1214/20-EJS1683

Primary: 60D05
Secondary: 55N20 , 60F17

Keywords: central limit theorem , Goodness-of-fit tests , persistent Betti number , Point processes , topological data analysis


Vol.14 • No. 1 • 2020
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