$U$-statistics are used to estimate a population parameter by averaging a function on a subsample over all the subsamples of the population. In this paper, the population we are interested in is formed by the entries of a row-column exchangeable matrix. We consider $U$-statistics derived from functions of quadruplets, i.e. submatrices of size $2 \times 2$. We prove a weak convergence result for these $U$-statistics in the general case and we establish a Central Limit Theorem when the matrix is also dissociated. Since row-column exchangeable matrices are an actual representation for exchangeable bipartite networks, we apply these results to statistical inference in network analysis.

翻译：美元-统计学用于估算人口参数,方法是在所有人口子抽样子抽样中平均使用一个函数。在本文中,我们感兴趣的人口是由一行可交换矩阵的条目组成的。我们考虑四极函数产生的美元-统计学,即大小为2美元/乘以2美元的子矩阵。我们证明,在一般情况下,这些美元-统计学的趋同结果是薄弱的,当矩阵分离时,我们建立了中央限制理论。由于行可交换矩阵是可交换的两边网络的实际代表,我们将这些结果应用于网络分析中的统计推断。