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Abstract:
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Spatial autoregressive (SAR) models have been widely used in analyses of economic, environmental data and recently social network data. Maximum likelihood estimation with the SAR models has been extensively studied and utilized. However, when dealing with large amount of data, direct evaluation of the log-likelihood function from the SAR models becomes computationally infeasible. To alleviate this challenge, we propose a randomized algorithm that provides an efficient way to obtain the maximum likelihood estimator, denoted as the randomized maximum likelihood estimator (RMLE). Numerical studies with simulated and real data are carried out to investigate the performance of the proposed algorithm. It is shown that the RMLE performs favorably in comparison with existing methods.
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