Primary Submission Category: Machine Learning and Causal Inference
Efficient, Cross-Fitting Estimation of Spatial Treatment Effects in Semiparametric Spatial Point Processes
Authors: Xindi Lin, Hyunseung Kang,
Presenting Author: Xindi Lin*
Recently, there has been great interest in studying causal relationships in spatial settings where the observed data are non-i.i.d., spatial points on a grid. This paper studies the efficient estimation of treatment effects in a semiparametric spatial point process where the target estimand is the effect of a spatial covariate on the spatial distribution of points, and we allow for nonparametric adjustment of measured confounders. We generalize cross-fitting to spatial point processes. In particular, we use random thinning, a popular procedure in simulations and Bayesian MCMC, to split the spatial data and use spatial composite likelihoods for estimation. We show that our estimator is consistent and asymptotically Normal where the asymptotic variance can be consistently estimated. We also show that the proposed estimator achieves the semiparametric efficiency bound if the spatial point process is Poisson. We demonstrate the performance of our proposed method through a simulation study and a re-analysis of the spatial distribution of tree species. We show that compared to existing approaches based on parametric models, our approach provides a more robust, flexible, and, in some cases, efficient estimate of the target estimand.