Preferential attachment is an appealing edge generating mechanism for modeling social networks. It provides both an intuitive description of network growth and an explanation for the observed power laws in degree distributions. However, there are often difficulties fitting parametric network models to data due to either model error or data corruption. In this paper, we consider semi-parametric estimation based on an extreme value approach that begins by estimating tail indices of the power laws of in- and out-degree for the nodes of the network using nodes with large in- and out-degree. This method uses tail behavior of both the marginal and joint degree distributions. We compare the extreme value method with the existing parametric approaches and demonstrate how it can provide more robust estimates of parameters associated with the network when the data are corrupted or when the model is misspecified.

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Keywords Estimation, Multivariate heavy-tailed statistics, Power laws, Preferential attachment, Regular variation
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Journal Extremes: statistical theory and applications in science, engineering and economics
Wan, P. (Phyllis), Wang, T. (Tiandong), Davis, R.A. (Richard A.), & Resnick, S.I. (2019). Are extreme value estimation methods useful for network data?. Extremes: statistical theory and applications in science, engineering and economics. doi:10.1007/s10687-019-00359-x