$U$-statistics on bipartite exchangeable networks
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2021
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| _version_ | 1866909063508393984 |
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| author | Minh, Tâm Le |
| author_facet | Minh, Tâm Le |
| contents | Bipartite networks with exchangeable nodes can be represented by row-column exchangeable matrices. A quadruplet is a submatrix of size $2 \times 2$. 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2103_12597 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | $U$-statistics on bipartite exchangeable networks Minh, Tâm Le Probability Statistics Theory Bipartite networks with exchangeable nodes can be represented by row-column exchangeable matrices. A quadruplet is a submatrix of size $2 \times 2$. 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. |
| title | $U$-statistics on bipartite exchangeable networks |
| topic | Probability Statistics Theory |
| url | https://arxiv.org/abs/2103.12597 |