  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.
