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Doubly-stochastic point processes model the occurrence of events over aspatial domain as an inhomogeneous Poisson process conditioned on therealization of a random intensity function. They are flexible tools forcapturing spatial heterogeneity and dependence. However, implementations ofdoubly-stochastic spatial models are computationally demanding, often havelimited theoretical guarantee, and/or rely on restrictive assumptions. Wepropose a penalized regression method for estimating covariate effects indoubly-stochastic point processes that is computationally efficient and doesnot require a parametric form or stationarity of the underlying intensity. Weestablish the consistency and asymptotic normality of the proposed estimator,and develop a covariance estimator that leads to a conservative statisticalinference procedure. A simulation study shows the validity of our approachunder less restrictive assumptions on the data generating mechanism, and anapplication to Seattle crime data demonstrates better prediction accuracycompared with existing alternatives.

A Penalized Poisson Likelihood Approach to High-Dimensional Semi-Parametric Inference for Doubly-Stochastic Point Processes