Doubly-stochastic point processes model the occurrence of events over a spatial domain as an inhomogeneous Poisson process conditioned on the realization of a random intensity function. They are flexible tools for capturing spatial heterogeneity and dependence. However, implementations of doubly-stochastic spatial models are computationally demanding, often have limited theoretical guarantee, and/or rely on restrictive assumptions. We propose a penalized regression method for estimating covariate effects in doubly-stochastic point processes that is computationally efficient and does not require a parametric form or stationarity of the underlying intensity. We establish the consistency and asymptotic normality of the proposed estimator, and develop a covariance estimator that leads to a conservative statistical inference procedure. A simulation study shows the validity of our approach under less restrictive assumptions on the data generating mechanism, and an application to Seattle crime data demonstrates better prediction accuracy compared with existing alternatives.

翻译：双重随机点过程将空间域上的事件发生建模为依赖于随机强度函数实现的非齐次泊松过程。这类模型是捕捉空间异质性与依赖性的灵活工具。然而，双重随机空间模型的实现通常计算成本高昂、理论保障有限，且/或依赖于严格假设。我们提出一种用于估计双重随机点过程中协变量效应的惩罚回归方法，该方法兼具计算高效性，且无需对基础强度函数设定参数形式或平稳性假设。我们建立了所提估计量的一致性与渐近正态性，并开发了可推导保守统计推断过程的协方差估计量。模拟研究表明，在更宽松的数据生成机制假设下，该方法具有有效性；应用于西雅图犯罪数据的实例表明，与现有替代方法相比，该方法具备更优的预测精度。