On the quality of eigenvector spatial filtering based parameter estimates for the normal probability model: implications about uncertainty and specification error for georeferenced data

Yongwan Chun¹ and Daniel A. Griffith²

_{1.  University of Texas at Dallas, 800 W. Campbell rd. Richardson, Texas75093, USA. ywchun@utdallas.edu}  

_{2. Ashbel Smith Professor, University of Texas at Dallas, 800 W. Campbell rd. Richardson, Texas 75093, USA.}

    _{dagriffith@utdallas.edu}

Abstract: Eigenvector spatial filtering, which introduces a subset of eigenvectors extracted from a spatial weights matrix as synthetic control variables in a regression model specification, furnishes a solution  to extraordinarily intricate statistical modeling problems involving spatial dependencies. It accounts for spatial autocorrelation in standard specifications of regression models. But the quality of the resulting regression parameter estimates has yet to be ascertained. The estimator properties to establish include unbiasedness, efficiency and consistency. The purpose of this paper is to demonstrate these estimator properties for linear regression parameters based on eigenvector spatial filtering, including a comparison with the simultaneous autoregressive (SAR) model. Eigenvector spatial filtering methodology requires the judicious selection of eigenvectors, whose number tends to increase with both level of linear regression residual spatial autocorrelation and number of areal units. A logistic regression description of the number of eigenvectors selected in a simulation pilot study suggests estimator consistency.

Keywords: Eigenvector spatial filtering, unbiasedness, efficiency, consistency.

from a spatial weights matrix as synthetic control variables in a regression model