U-Statistics on bipartite exchangeable networks

Author:

Le Minh TâmORCID

Abstract

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.

Funder

Conseil Régional, Île-de-France

Agence Nationale de la Recherche

Publisher

EDP Sciences

Subject

Statistics and Probability

Reference67 articles.

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