Third Year Candidacy Presentation: Statistical Inference for Subgraph Densities Under Induced Random Sampling from Network Data

Ayoushman Bhattacharya, PhD Student at Washington University in St. Louis

In this talk, we develop a framework for obtaining statistical guarantees for subgraph densities of a general population network under without replacement sampling (SRSWOR). Under this sampling scheme, we establish the asymptotic normality of the Horvitz-Thompson (HT) estimator for the population subgraph densities with minimal assumptions. We also establish the joint asymptotic normality of two subgraph densities, which is crucial in establishing weak convergence of the global transitivity of the sampled graph. To facilitate the inferential procedures, we provide a jackknife and a bootstrap estimator of the unknown population variance and establish its consistency. Our results find a useful application to the problem of testing the equality of two population graphs using the subgraph densities as the test statistic. Finally, we present a simulation study and a real data analysis that corroborate our theoretical findings.

Advisor: Soumen Lahiri

This talk will also be available via Zoom:

https://wustl.zoom.us/j/93325571542?pwd=5GdaLtGxUuQyZAY1Oip3pm0FiOYa1c.1

Meeting ID: 933 2557 1542

Passcode: 428363