Influence diagnostics in Gaussian spatial linear models

Abstract

Spatial linear models have been applied in numerous fields such as agriculture, geoscience and environmental sciences, among many others. Spatial dependence structure modelling, using a geostatistical approach, is an indispensable tool to estimate the parameters that define this structure. However, this estimation may be greatly affected by the presence of atypical observations in the sampled data. The purpose of this paper is to use diagnostic techniques to assess the sensitivity of the maximum-likelihood estimators, covariance functions and linear predictor to small perturbations in the data and/or the spatial linear model assumptions. The methodology is illustrated with two real data sets. The results allowed us to conclude that the presence of atypical values in the sample data have a strong influence on thematic maps, changing the spatial dependence structure.

Keywords:

• spatial statistics
• Gaussian models
• influence diagnostics and precision agriculture

Acknowledgements

The authors thank the Editor-in-Chief and two referees for the useful comments which improved our paper. We also acknowledge the partial financial support from Projects DIPUV 11/2006, Universidad de Valparaíso, and Fondecyt 1070919, Chile, and Fundaço Araucária do State of Paraná and CNPq, Brazil.