Dissertation Title: Linear and Nonlinear Estimation with Spatial Data

Chapter 1 Pseudo Generalized Least Squares Regression Estimation with Spatial Data Abstract It is hard to account for all pairwise correlations in the estimation of the mean parameters for a large sample of spatial data. In a linear regression model, a pseudo generalized least squares (PGLS) approach is proposed. Data could be divided into groups according to natural geographic areas, only correlations within groups are accounted for. Since correlations within groups account for most of the correlations among observations, the resulting PGLS estimator will not lose much efficiency compared to GLS. The PGLS estimator is consistent and asymptotically normal, and computationally easier than GLS. A HAC variance covariance estimator which is robust to both heteroskedasticity and spatial correlation is provided. Moreover, a convenient way of using the OLS residuals to calculate the spatial correlation parameters is also proposed, which is very easy and works well as shown in the simulation. Simulation study also shows that PGLS is more efficient than OLS under certain conditions. This paper also gives an empirical example on estimating policy effects on student performance accounting for the correlations among schools within the same school districts.