Functional central limit theorems for persistent Betti numbers on cylindrical networks

被引：7

作者：

Krebs, Johannes ^{[1
]}

Hirsch, Christian ^{[2
]}

机构：

[1] Heidelberg Univ, Inst Appl Math, Neuenheimer Feld 205, D-69120 Heidelberg, Germany

[2] Aarhus Univ, Dept Math, Aarhus, Denmark

来源：

SCANDINAVIAN JOURNAL OF STATISTICS | 2022年 / 49卷 / 01期

关键词：

functional central limit theorems; goodness‐ of‐ fit tests; graphical networks; persistent Betti numbers; stochastic geometry; topological data analysis; MINIMAL SPANNING-TREES; CONVERGENCE;

D O I：

10.1111/sjos.12524

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

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 Cech 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.

引用

页码：427 / 454

页数：28

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