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 correlation. 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：双随机点过程将空间域上的事件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，是捕捉空间异质性和相关性的灵活工具。然而，现有双随机空间模型的实现存在计算负担重、理论保证有限或依赖严格假设等问题。本文提出一种用于估计双随机点过程中协变量效应的惩罚回归方法，该方法计算高效且无需假定底层强度的参数形式或平稳性。我们的方法基于对真实连续随机强度函数的近似离散确定性表示。研究表明，尽管存在模型误设，协变量效应估计仍可实现一致性和渐近正态性，并开发了能产生有效（虽具有保守性）统计推断过程的协方差估计量。数值模拟验证了该方法在较宽松数据生成机制假设下的有效性，应用于西雅图犯罪数据的实例表明，与现有替代方法相比，本方法具有更优的预测精度。