In this paper we consider a dynamic Erd\H{o}s-R\'enyi graph in which edges, according to an alternating renewal process, change from present to absent and vice versa. The objective is to estimate the on- and off-time distributions while only observing the aggregate number of edges. This inverse problem is dealt with, in a parametric context, by setting up an estimator based on the method of moments. We provide conditions under which the estimator is asymptotically normal, and we point out how the corresponding covariance matrix can be identified. It is also demonstrated how to adapt the estimation procedure if alternative subgraph counts are observed, such as the number of wedges or triangles.

翻译：本文研究一类动态Erdős-Rényi图模型，其中边依据交替更新过程在存在与缺失状态间切换。研究目标是在仅能观测总边数的情况下，估计边的连通时间与断开时间分布。该反问题在参数化框架下通过矩估计方法构建估计量进行处理。我们给出了估计量渐近正态的充分条件，并指出如何确定相应的协方差矩阵。同时论证了当观测其他子图计数（如楔形结构或三角形数量）时，如何调整估计程序。