Affiliation networks with an increasing degree sequence. Issue 22 (17th November 2017)

• Record Type: Journal Article
• Authors: Zhang, Yong; Qian, Xiaodi; Qin, Hong; Yan, Ting
• Is Part Of: Communications in statistics. Volume 46:Issue 22(2017)
• Page Start: 11163
• Page End: 11180
• Publication Date: 2017-11-17
• Subjects: Affiliation networks -- Asymptotic normality -- Consistency -- Maximum likelihood estimators.; 62E20 -- 62F12; Mathematical statistics -- Periodicals; Mathematics; Statistics; 519.2
• DOI: 10.1080/03610926.2016.1260741
• Languages: English
• ISSNs: 0361-0926

Abstract

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.