$U$-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. We shed further light on these results using the Aldous-Hoover representation theorem for row-column exchangeable random variables. Finally, to illustrate these results, we give examples of hypothesis testing for bipartite networks.

翻译：以美元统计来估计人口参数,方法是在人口的所有子抽样中平均使用一个子抽样的函数。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。我们考虑由四极函数产生的美元统计,即大小为2美元乘以2美元的亚梯子。在一般情况下,我们证明这些美元统计在一般情况下的趋同效果微弱,当矩阵分离时,我们建立了中央限制理论。我们用Aldous-Hoover表示的可交换随机变量来进一步说明这些结果。最后,为了说明这些结果,我们举例说明两极网络的假设测试。