Assessment of local influence in spatial elliptical linear measurement error models

Abstract

In this paper, we consider estimation and inference procedures in spatial linear models when some of the covariates are measured with errors. It is assumed that the additive error distributed according to the law belonging to the class of elliptically contoured distributions. The development of the corrected score function with the family of elliptical distributions is the basis for derivation of the estimators. For sensitivity analysis, the local influence approach is used for assessing influence of small perturbations on the parameter estimates. A simulation study is presented illustrating the good performance of the proposed approach, including the robustness property for the heavier tail models. We further illustrate the proposed procedures by an application in a real dataset.

Keywords:

• Geostatistics
• global influence
• spatial variability
• elliptical distribution
• measurement error

Acknowledgments

The authors are grateful to the Editor, Associate Editor, and two referees for their helpful comments on an earlier version of this paper.