We propose an autoregressive framework for modelling dynamic networks with dependent edges. It encompasses models that accommodate, for example, transitivity, degree heterogenenity, and other stylized features often observed in real network data. By assuming the edges of networks at each time are independent conditionally on their lagged values, the models, which exhibit a close connection with temporal exponential random graph models, facilitate both simulation and the maximum likelihood estimation (MLE) in a straightforward manner. Due to the possibly large number of parameters in the models, the natural MLEs may suffer from slow convergence rates. An improved estimator for each component parameter is proposed based on an iteration employing projection, which mitigates the impact of the other parameters. Leveraging a martingale difference structure, the asymptotic distribution of the improved estimator is derived without the assumption of stationarity. The limiting distribution is not normal in general, although it reduces to normal when the underlying process satisfies some mixing conditions. Illustration with a transitivity model was carried out in both simulation and a real network data set.

Publication:

JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY

http://dx.doi.org/10.1093/jrsssb/qkag063

Author:

Jinyuan Chang

Joint Laboratory of Data Science and Business Intelligence, Institute of Statistical Interdisciplinary Research, Southwestern University of Finance and Economics, Chengdu, China

State Key Laboratory of Mathematical Sciences, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China

Qin Fang

Business School, The University of Sydney, Sydney, Australia

Eric D. Kolaczyk

Department of Mathematics and Statistics, McGill University, Montreal, Canada

Address for correspondence: Eric D. Kolaczyk, Department of Mathematics and Statistics, McGill University, 805 Sherbrooke St W, Montreal, Quebec, Canada H3A 0B9

Email: eric.kolaczyk@mcgill.ca

Peter W. MacDonald

Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, Canada

Qiwei Yao

Department of Statistics, The London School of Economics and Political Science, London, UK

Address for correspondence: Eric D. Kolaczyk, Department of Mathematics and Statistics, McGill University, 805 Sherbrooke St W, Montreal, Quebec, Canada H3A 0B9. Email: eric.kolaczyk@mcgill.ca