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Asymptotic analysis of tail index estimation for network data
Real-life networks like online communities or citation relationsships are often observed to be approximately scale-free, meaning that the empirical degree distrubition has a regularly varying behavior. In theory, this fact is reflected for example by the class of preferential attachment models. The index of regular variation is an important parameter to describe the extremal behavior of those models and thus an important quantity to estimate from network data, often estimated by methods developed for i.i.d. data like the famous Hill-estimator. However, since network data is non-i.i.d., an in particular the largest nodes have a strong asymptotic dependence structure, the asymptotic behavior of those estimators is largely unknown, with so far only a few consistency results available. The aim of this project is to develop concentrations inequalities tailored to the tails of the joint distribution of largest nodes that allow us to derive finer results like asymptotic normality of estimators.

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