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.

近几十年来，用于减少样本量的新技术的发展吸引了越来越多的兴趣。最近的发现使我们能够通过所谓的有效样本量（ESS）来量化空间数据样本中重复信息的数量，有效样本量（ESS）的定义来自与最大似然估计相关的Fisher信息。但是，在样本量非常大的所有情况下，从计算角度来看，最大似然估计和ESS评估都是具有挑战性的。根据来自块似然估计方法的Godambe信息，提出了ESS的另一种定义。研究了该数量满足的几个理论特性。我们的建议是在一些参数相关结构中进行评估的，包括内部类，AR（1），Matten，和同时自回归模型。仿真实验表明，我们的建议提供了基于全似然性的ESS的准确近似值，同时保持了适度的计算成本。对大型数据集进行分析以量化所提出框架在实践中的有效性和局限性。