U -Statistics on bipartite exchangeable networks
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 quadruple...
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| Published in | Probability and statistics Vol. 27; pp. 576 - 620 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
2023
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| Online Access | Get full text |
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| Summary: | 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. |
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| ISSN: | 1262-3318 1262-3318 |
| DOI: | 10.1051/ps/2023010 |