Distributed Estimation and Inference for Spatial Autoregression Model with Large Scale Networks

Xuening Zhu is currently an associate professor in School of Data Science at Fudan University. She got her Ph.D. degree in Economics (Statistics) from Guanghua School of Management, Peking University in 2017. During 2017-2018 she worked as a postdoctoral research assistant in Department of Statistics, Penn State University. Her research interests are mainly on network data modelling and business statistics. Her research has been published in Journal of Econometrics, Journal of the American Statistical Association, Annals of Statistics.

The rapid growth of online network platforms generates large scale network data and it poses great challenges for statistical analysis using the spatial autoregression (SAR) model. In this work, we develop a distributed estimation and statistical inference framework for the SAR model on a distributed system. We first propose a distributed network least squares approximation (DNLSA) method. This enables us to obtain a one-step estimator by taking a weighted average of local estimators on each worker. Afterwards, a refined two-step estimation is designed to further reduce the estimation bias. For statistical inference, we utilize a random projection method to reduce the expensive communication cost. Theoretically, we show the consistency and asymptotic normality of both the one-step and two-step estimators. In addition, we provide theoretical guarantee of the distributed statistical inference procedure. The theoretical findings and computational advantages are validated by several numerical simulations implemented on the Spark system. Lastly, an experiment on the Yelp dataset further illustrates the usefulness of the proposed methodology.