线性偏好依恋模型的拟合
Fitting the Linear Preferential Attachment Model
摘要：
偏好连接是一种很有吸引力的机制，可以用来模拟有向社交网络中度分布的幂律行为。在本文中，我们考虑的方法拟合一个5参数线性偏好模型的网络数据下的两个数据场景。在网络形成的完整历史的情况下，我们推导出参数的极大似然估计，并证明它是强相合和渐近正态的。在只有网络的单次快照的情况下，我们提出了一种估计方法，它结合了矩量法与近似的可能性。由此产生的估计量也是强一致的，并且与MLE估计量相比表现得相当好。我们通过模拟数据说明了这两种估计过程，并探讨了该模型在真实数据示例中的使用。
英文摘要：
Preferential attachment is an appealing mechanism for modeling power-law behavior of the degree distributions in directed social networks. In this paper, we consider methods for fitting a 5-parameter linear preferential model to network data under two data scenarios. In the case where full history of the network formation is given, we derive the maximum likelihood estimator of the parameters and show that it is strongly consistent and asymptotically normal. In the case where only a single-time snapshot of the network is available, we propose an estimation method which combines method of moments with an approximation to the likelihood. The resulting estimator is also strongly consistent and performs quite well compared to the MLE estimator. We illustrate both estimation procedures through simulated data, and explore the usage of this model in a real data example.
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