Abstract: This article considers an empirical likelihood method for data located on a spatial grid. The method allows inference on spatial parameters, such as means and variograms, without knowledge of the underlying spatial dependence structure. Log-likelihood ratios are shown to have chi-square limits under spatial dependence for calibrating tests and confidence regions, and maximum empirical likelihood estimators permit parameter estimation and testing of spatial moment conditions. A practical Bartlett correction is proposed to improve the coverage accuracy of confidence regions. The spatial empirical likelihood method is investigated through a simulation study and illustrated with a data example.
Key words and phrases: Data blocking, discrete index random fields, estimating equations.