| Issue |
ESAIM: PS
Volume 27, 2023
|
|
|---|---|---|
| Page(s) | 576 - 620 | |
| DOI | https://doi.org/10.1051/ps/2023010 | |
| Published online | 16 June 2023 | |
U-Statistics on bipartite exchangeable networks
Université Paris-Saclay, AgroParisTech, INRAE, UMR MIA Paris-Saclay, 91120 Palaiseau, France
* Corresponding author: tam.le-minh@inrae.fr
Received:
16
December
2021
Accepted:
27
April
2023
Bipartite networks with exchangeable nodes can be represented by row-column exchangeable matrices. A quadruplet is a submatrix of size 2 × 2. A quadruplet U-statistic is the average of a function on a quadruplet over all the quadruplets of a matrix. We prove several asymptotic results for quadruplet U-statistics on row-column exchangeable matrices, including a weak convergence result in the general case and a central limit theorem when the matrix is also dissociated. These results are applied to statistical inference in network analysis. We suggest a method to perform parameter estimation, network comparison and motifs count for a particular family of row-column exchangeable network models: the bipartite expected degree distribution (BEDD) models. These applications are illustrated by simulations.
Mathematics Subject Classification: 60F05 / 60G09 / 62G20
Key words: U-statistics / row-column exchangeability / central limit theorem / network inference
© The authors. Published by EDP Sciences, SMAI 2023
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