Studies Of Degree-based Models In Affiliation Networks

Affiliation network(also called a two-mode network)is one type of network data.It composes of two sets of different node sets(a set of actors and a set of social events),in which actors belong to events.Although some statistical models have been proposed to analyze the affiliation networks,the asymptotic property of the estimator is still unknown or has not been properly explored.In this thesis,we first propose an affiliation network model based on node de-grees.In this model,the node degrees are the exclusively sufficient statistics in the exponential family distributions on graphs.It models the heterogeneity of the node degrees.We study the maximum likelihood estimation for model parameter-s.Second,when the number of nodes goes to infinity,we prove the consistency of maximum likelihood estimators by obtaining the fast convergence rate of Newton iterative sequences.Finally,we obtain the central limit theorem of the maximum likelihood estimator by deriving the approximate inverse matrix of the Fisher infor-mation matrix.We study the finite sample numerical simulations and provide a real data analysis.Numerical simulation results show that theoretical results provide good approximation for the finite sample case.