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The rapid growth of online network platforms generates large-scale networkdata and it poses great challenges for statistical analysis using the spatialautoregression (SAR) model. In this work, we develop a novel distributedestimation and statistical inference framework for the SAR model on adistributed system. We first propose a distributed network least squaresapproximation (DNLSA) method. This enables us to obtain a one-step estimator bytaking a weighted average of local estimators on each worker. Afterwards, arefined two-step estimation is designed to further reduce the estimation bias.For statistical inference, we utilize a random projection method to reduce theexpensive communication cost. Theoretically, we show the consistency andasymptotic normality of both the one-step and two-step estimators. In addition,we provide theoretical guarantee of the distributed statistical inferenceprocedure. The theoretical findings and computational advantages are validatedby several numerical simulations implemented on the Spark system. Lastly, anexperiment on the Yelp dataset further illustrates the usefulness of theproposed methodology.

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