Spatial regression models are central to the field of spatial statistics. Nevertheless, their estimation in case of large and irregular gridded spatial datasets presents considerable computational challenges. To tackle these computational problems, Arbia \citep{arbia_2014_pairwise} introduced a pseudo-likelihood approach (called pairwise likelihood, say PL) which required the identification of pairs of observations that are internally correlated, but mutually conditionally uncorrelated. However, while the PL estimators enjoy optimal theoretical properties, their practical implementation when dealing with data observed on irregular grids suffers from dramatic computational issues (connected with the identification of the pairs of observations) that, in most empirical cases, negatively counter-balance its advantages. In this paper we introduce an algorithm specifically designed to streamline the computation of the PL in large and irregularly gridded spatial datasets, dramatically simplifying the estimation phase. In particular, we focus on the estimation of Spatial Error models (SEM). Our proposed approach, efficiently pairs spatial couples exploiting the KD tree data structure and exploits it to derive the closed-form expressions for fast parameter approximation. To showcase the efficiency of our method, we provide an illustrative example using simulated data, demonstrating the computational advantages if compared to a full likelihood inference are not at the expenses of accuracy.

翻译：空间回归模型是空间统计领域的核心工具。然而，当处理大规模且非规则格网化的空间数据集时，这类模型的估计面临着巨大的计算挑战。为解决这些计算问题，Arbia（2014）提出了一种伪似然方法（称为成对似然，简称PL），该方法需要识别内部相关但条件互不相关的观测对。然而，尽管PL估计量具有最优的理论性质，但在处理非规则格网数据时，其实际实现（涉及观测对的识别）会遭遇显著的计算难题，在多数实证案例中，这些难题反而抵消了其优势。本文提出了一种专门用于简化大规模非规则格网空间数据中PL计算的算法，极大简化了估计阶段。具体而言，我们聚焦于空间误差模型（SEM）的估计。所提出的方法利用KD树数据结构高效配对空间耦合单元，并推导出用于快速参数近似的闭式表达式。为展示该方法的效率，我们通过模拟数据示例证明了其计算优势——与完全似然推断相比，并未以牺牲精度为代价。