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, existing 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. Our approach is based on an approximate (discrete and deterministic) formulation of the true (continuous and stochastic) intensity function. We show that consistency and asymptotic normality of the covariate effect estimates can be achieved despite the model misspecification, and develop a covariance estimator that leads to a valid, albeit 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内事件的发生建模为以随机强度函数实现为条件的非齐次泊松过程。它们是捕捉空间异质性和依赖性的灵活工具。然而，现有双重随机空间模型的实现计算成本高昂，通常理论保证有限，且/或依赖于限制性假设。我们提出一种惩罚回归方法，用于估计双重随机点过程中的协变量效应，该方法计算高效，且不需要基础强度的参数形式或平稳性假设。我们的方法基于对真实（连续且随机）强度函数的近似（离散且确定性）表述。我们证明，尽管存在模型误设，协变量效应估计仍能达到一致性和渐近正态性，并开发了一种协方差估计器，从而导出一个有效（尽管保守）的统计推断程序。模拟研究表明，在数据生成机制限制较少的假设下，我们的方法具有有效性；西雅图犯罪数据的应用则显示，与现有替代方法相比，本方法具有更好的预测准确性。