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Affiliation weighted networks with a differentially private degree sequence. (English) Zbl 1483.62199

Summary: 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. The asymptotic theorem of a differentially private estimator of the parameter in the private \(p_0\) model has been established. However, the \(p_0\) model only focuses on binary edges for one-mode network. In many case, the connections in many affiliation networks (two-mode) could be weighted, taking a set of finite discrete values. In this paper, we derive the consistency and asymptotic normality of the moment estimators of parameters in affiliation finite discrete weighted networks with a differentially private degree sequence. Simulation studies and a real data example demonstrate our theoretical results.

MSC:

62P25 Applications of statistics to social sciences
62E20 Asymptotic distribution theory in statistics
62F12 Asymptotic properties of parametric estimators
91D30 Social networks; opinion dynamics
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