Two Stage Estimation Procedure of Non-Linear Regression Functions for Spatially-Dependent Data

Abstract

This paper considers parameter estimation of regression models for spatial data. It is well-known that good prediction for the target variable needs incorporation of effects from neighbor cells. However, this is not an easy task in modeling and parameter estimation. We consider estimation for deforestation model, where forest areal ratios are regressed by human population densities and relief energies. The two-stage method proposed here is: 1) Find the best non-linear regression function of explanatory variables under independence assumption. 2) Predict target values by the estimated function. 3) Obtain the final prediction by correction based on linear regression with center's and neighbors' predicted values. The method is an extension of our pseudo maximum likelihood method reported at IGARSS 2019. By an application to actual data, it worked very well and successfully clarified the difference of neighbors' effects of explanatory variables. Note that the method is applicable in a general setting.