# Affiliation networks with an increasing degree sequence

## TL;DR

This paper investigates the asymptotic properties of estimators in affiliation networks with increasing size, establishing their consistency and normality, supported by simulations and real data.

## Contribution

It introduces a new affiliation model based on degree sequences and proves the asymptotic behavior of its maximum likelihood estimator.

## Key findings

- MLE is uniformly consistent and asymptotically normal
- Simulation studies confirm theoretical results
- Real data example supports model validity

## 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.