A0180
Title: Functional principal component analysis of spatially and temporally indexed point processes
Authors: Yehua Li - University of California at Riverside (United States) [presenting]
Abstract: Spatially and temporally indexed point process data is modeled as a multi-level log-Gaussian Cox process where the log intensity function depends on a partially linear single-index structure of spatio-temporal covariates and three latent functional random effects representing the spatial and temporal random effects as well as their interactions. It is assumed that the latent functional effects are Gaussian processes with Karhunen-Loeve representations, and the unknown link function of the single-index as well as the covariance functions of the latent functional effects as splines, are modeled. The proposal is to estimate the partially linear coefficients and the single-index link function using a Poisson maximum likelihood method and the covariance functions of the latent processes using maximum composite likelihood methods. Approaches to predict the functional principal component scores are also proposed. Under the multi-level dependence structure and allowing the spatiotemporal covariates to be non-stationary, the proposed estimators follow rather unconventional convergence rates, which depend on both the number of locations and the number of repeated measures in time. The proposed method is illustrated through a simulation study and a real-data application in modeling bike-sharing events.
