A Penalized Poisson Likelihood Approach to High-Dimensional Semiparametric Inference of Doubly-Stochastic Point Processes

• Activity Number: 204 - Statistical Computing by Deep Learning and Penalization
• Type: Contributed
• Date/Time: Monday, August 8, 2022 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistical Computing
• Author(s): Si Cheng* and Ali Shojaie
• Companies: University of Washington and University of Washington
• Keywords: Cox process; spatial point process; semi-parametric model; high-dimensional inference; non-stationarity

Abstract

Doubly-stochastic point processes model the occurrence of events over a spatial domain as an inhomogeneous Poisson process conditioning on the realization of a random intensity function, and are flexible tools for capturing spatial heterogeneity and dependence. However, their implementations are computationally demanding, have limited theoretical guarantee, and/or rely on restrictive assumptions. We propose a penalized regression method for doubly-stochastic point processes that is computationally efficient and does not require a parametric form or stationarity for the underlying intensity. We establish the consistency of the proposed estimator and develop an asymptotically valid statistical inference procedure. Simulation and an application to Seattle crime data illustrate the improved prediction accuracy, better type I error control and reasonable inferential power of our approach compared with existing ones.