Abstract

The development of new techniques for sample size reduction has attracted growing interest in recent decades. Recent findings allow us to quantify the amount of duplicated information within a sample of spatial data through the so-called effective sample size (ESS), whose definition arises from the Fisher information that is associated with maximum likelihood estimation. However, in all circumstances where the sample size is very large, maximum likelihood estimation and ESS evaluation are challenging from a computational viewpoint. An alternative definition of the ESS, in terms of the Godambe information from a block likelihood estimation approach, is presented. Several theoretical properties satisfied by this quantity are investigated. Our proposal is evaluated in some parametric correlation structures, including the intraclass, AR(1), Matérn, and simultaneous autoregressive models. Simulation experiments show that our proposal provides accurate approximations of the full likelihood-based ESS while maintaining a moderate computational cost. A large dataset is analyzed to quantify the effectiveness and limitations of the proposed framework in practice.