The Contest between MLE, GMM, and Subsampling for Huge Spatial Autoregressive Models

• Activity Number: 403
• Type: Contributed
• Date/Time: Wednesday, August 10, 2005 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistics and the Environment
• Author(s): Janette Walde*+ and Mario Larch and Gottfried Tappeiner
• Companies: University of Innsbruck and University of Innsbruck and University of Innsbruck
• Keywords: Spatial Statistics ; GMM estimation ; Subsampling

Abstract

This paper analyzes the estimator that is most suitable for spatial problems with huge spatial weighting matrices. For estimation, we use different methodologies. To account for the numerical difficulties of computing the logarithm of the determinant of the Jacobian regarding the maximum likelihood estimation, we employ various decompositions/approximation techniques (e.g., the eigenvalue approach). More recent suggestions count on the sparsity of the weighting matrix and apply a Cholesky or LU decomposition. However, sparsity is not a compulsory property. Two feasible approaches for handling large datasets are developed by Barry and Pace (1999) and Smirnov and Anselin (2000). An alternative way to overcome both the computational problems and the limitation on the normality assumption is the approach of the generalized method of moments suggested by Kelejian and Prucha (1999). Their proposed estimators are simple to implement and computationally much easier to handle. However, for huge sample sizes, all approaches have severe computational problems.