Title: Affiliation networks with an increasing degree sequence,
Abstract: Affiliation network is one kind of two-mode social network with two different
sets of nodes (namely, a set of actors and a set of social events) and edges
representing the affiliation of the actors with the social events. Although a
number of statistical models are proposed to analyze affiliation networks, the
asymptotic behaviors of the estimator are still unknown or have not been
properly explored. In this paper, we study an affiliation model with the degree
sequence as the exclusively natural sufficient statistic in the exponential
family distributions. We establish the uniform consistency and asymptotic
normality of the maximum likelihood estimator when the numbers of actors and
events both go to infinity. Simulation studies and a real data example
demonstrate our theoretical results.