The Buckley-Osthus model and the block preferential attachment model: statistical analysis and application

This paper is concerned with statistical estimation of two preferential attachment models: the Buckley-Osthus model and the hierarchical preferential attachment model. We prove that the maximum likelihood estimates for both models are consistent. We perform simulation studies to corroborate our theoretical findings. We also apply both models to study the evolution of a real-world network. A list of open problems are presented.