Abstract: We develop an empirical likelihood (EL) method for inference over a broad class of spatial data exhibiting stochastic spatial patterns with various levels of infill sampling. Without stringent assumptions about the sampling design or spatial dependence, the EL method (based on estimating functions) produces log-likelihood ratio statistics having chi-square limits for calibrating tests and confidence regions for spatial parameters. Maximum EL estimators are valid for point estimation and formulating tests of spatial structure conditions. The proposed EL approach applies additionally to inference in spatial regression models with irregularly located sampling sites. The method is illustrated with a data example and investigated through simulation for calibrating confidence intervals and goodness-of-fit tests.

Key words and phrases: Blockwise empirical likelihood, infill sampling, spatial regression, stationarity, stochastic sampling.