We propose a random forest estimator for the intensity of spatial point processes, applicable with or without covariates. It retains the well-known advantages of a random forest approach, including the ability to handle a large number of covariates, out-of-bag cross-validation, and variable importance assessment. Importantly, even in the absence of covariates, it requires no border correction and adapts naturally to irregularly shaped domains and manifolds. Consistency and convergence rates are established under various asymptotic regimes, revealing the benefit of using covariates when available. Numerical experiments illustrate the methodology and demonstrate that it performs competitively with state-of-the-art methods.

翻译：本文提出一种适用于空间点过程强度的随机森林估计器，无论是否存在协变量均可应用。该方法保留了随机森林方法的显著优势，包括处理大量协变量的能力、袋外交叉验证以及变量重要性评估。重要的是，即使在无协变量的情况下，该方法无需边界校正，且能自然地适应不规则形状域和流形。我们在多种渐近机制下建立了该估计器的一致性和收敛速率，揭示了在可用时利用协变量的益处。数值实验展示了该方法论，并证明其性能与前沿方法具有竞争力。