Semiparametric modeling and analysis for longitudinal network data

Yinqiu He, Jiajin Sun, Yuang Tian, Zhiliang Ying, Yang Feng

The Annals of Statistics · 2025 · Volume 53 · Issue 4

Abstract

We introduce a semiparametric latent space model for analyzing longitudinal network data. The model consists of a static latent space component and a time-varying node-specific baseline component. We develop a semiparametric efficient score equation for the latent space parameter by adjusting for the baseline nuisance component. Estimation is accomplished through a one-step update estimator and an appropriately penalized maximum likelihood estimator. We derive oracle error bounds for the two estimators and address identifiability concerns from a quotient manifold perspective. Our approach is demonstrated using the New York Citi Bike Dataset.

Keywords

05C82, 62F12, 62H12, 91D30, Heterogeneity, Latent space model, low rank, network, Poisson counting process, semiparametric

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