Department seminar by Tiandong Wang, Cornell UniversityExport this event to calendar

Friday, January 11, 2019 — 4:00 PM EST

ESTIMATION IN PREFERENTIAL ATTACHMENT NETWORKS


Preferential attachment is widely used to model power-law behavior of degree distributions in both directed and undirected networks. Statistical estimates of the tail exponent of the power-law degree distribution often use the Hill estimator as one of the key summary statistics, even though the consistency of the Hill estimator for network data has not been explored. We derive the asymptotic behavior of the joint degree sequences by embedding the in- and out-degrees of a xed node into a pair of switched birth processes with immigration
and then establish the convergence of the joint tail empirical measure. From these steps, the consistency of the Hill estimators is obtained.

Meanwhile, one important practical issue of the tail estimation problem is how to select a threshold above which observations follow a power-law distribution. A minimum distance selection procedure (MDSP) has been widely adopted, especially in the analyses of social networks. However, theoretical justications on this selection procedure remain scant. We then study the asymptotic behavior of the optimal threshold and the corresponding power-law index given by the MDSP. We also nd that the MDSP tends to choose too high a threshold level and leads to Hill estimates with large variances and root mean squared errors for simulated data with Pareto-like tails. 

Note: This is based on joint works with S.I. Resnick (Cornell University, US), H. Drees (University of Hamburg, Germany) and A. Janen (KTH Royal Institute of Technology, Sweden).

Location 
M3 - Mathematics 3
Room: 3127
200 University Avenue West

Waterloo, ON N2L 3G1
Canada

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