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 article, 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.

KEYWORDS:

• Affiliation networks
• Asymptotic normality
• Consistency
• Maximum likelihood estimators.

MATHEMATICS SUBJECT CLASSIFICATION:

• 62E20
• 62F12

Acknowledgments

We are very grateful to one anonymous referee and the editor for their valuable comments that have greatly improved the manuscript.

Funding

Qin's research is partially supported by the National Natural Science Foundation of China (No.11271147, 11471135). Yan's research is partially supported by the National Natural Science Foundation of China (No.11401239) and the self-determined research funds of CCNU from the colleges's basic research and operation of MOE (CCNU15A02032, CCNU15ZD011) and a fund from KLAS (130026507). Zhang's research is supported by a fund from CCNU (2016CXZZ157).