Indicator Variables in Spatial Prediction When Σ Is Unknown

Abstract

The use of indicator variables for computing predictions for the linear model is a well known technique. Fuller (Fuller, W. A. (1980). The use of indicator variables in computing predictions. J. Econometrics2: 231–243.) extends this to predictions for models with a general covariance structure and nonlinear models. In this work we use indicator variables for spatial data models with trend and a parametrized but unknown covariance function. We show that Restricted Maximum Likelihood (REML) estimates are a natural way to estimate the covariance parameters under this schema. We use dummy variables to predict the response at any number of sites, on a random Gaussian field. A simulation study was conducted to study the performance of the estimate and predictor when we consider indicator variables in the model.

Keywords:

• Restricted maximum likelihood estimation
• Maximum likelihood estimations
• Indicator variables
• Spatial models

Acknowledgments

We are grateful to S. Pantula for his comments and careful suggestions. This research is supported by Consejo Nacional de Ciencia y Tecnologi′a grant 32393-E. The authors also wish to express their gratitude to the editor and referee for their helpful comments.

Notes

^aWe used our own code as well as commercial software with GLS routines for special covariance structures, and REML and ML methods for estimation of covariance parameters.