The asymptotic normality of the fixed number of the maximum likelihood estimators (MLEs) in the directed finite weighted network models with an increasing bi-degree sequence has been established recently. In this article, we further derive the central limit theorem for linear combinations of all the MLEs with an increasing dimension when the edges take finite discrete weight. Simulation studies are provided to illustrate the asymptotic results.

中文翻译：

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具有双学位序列的有向有限加权随机图的渐近分布

最近已经建立了双向次数增加的定向有限加权网络模型中最大数目似然估计器（MLE）的固定数量的渐近正态性。在本文中，我们进一步推导了当边缘采取有限离散权重时，所有MLE的线性组合的中心极限定理，且其维数不断增加。提供仿真研究来说明渐近结果。