Heavy Tail Phenomena in in Preferential Attachment Networks

Wang, Tiandong

Heavy Tail Phenomena in in Preferential Attachment Networks

Abstract

Preferential attachment is widely used to model the power-law behavior of degree distributions in social networks. In this thesis, we study three aspects of a directed preferential attachment model. First, we consider fitting this network model under different data scenarios. We propose both parametric and semi-parametric estimation procedures and compare the corresponding estimating results. Second, we see from empirical studies that statistical estimates of the marginal tail exponent of the power-law degree distribution often use the Hill estimator, even though no theoretical justification has been given. Hence, we study the convergence of the joint empirical measure for in- and out-degrees and prove the consistency of the Hill estimator for the preferential attachment model. Finally, we consider a widely adopted threshold selection procedure when estimating the power-law index in practice and examine the asymptotic behavior of the selected threshold as well as the corresponding power-law index given.

Date Issued

2019-08-30

Keywords

Statistics; Estimation; Hill estimators; multivariate heavy tail statistics; power laws; preferential attachment; Operations research

Committee Chair

Resnick, Sidney Ira

Committee Member

Jarrow, Robert A.
Wells, Martin Timothy

Degree Discipline

Operations Research and Information Engineering

Degree Name

Ph.D., Operations Research and Information Engineering

Degree Level

Doctor of Philosophy

Types

dissertation or thesis