Title: Point process regression
Authors: Alvaro Gajardo - University of California Davis (United States) [presenting]
Hans-Georg Mueller - University of California Davis (United States)
Abstract: Point processes in time have a wide range of applications such as the number of COVID-19 confirmed cases in a country or the claims arrival process in insurance, among many others. Due to advances in technology, such samples of point processes are increasingly encountered. They are being recorded along with covariates, which contain intrinsic characteristics related to each realization of the process. A key feature of interest is the local intensity function, which measures the rate of occurrence of events per unit time and allows to explore point process data. We consider a novel non-parametric functional regression approach for replications of Cox processes as responses with vector covariates as predictors, which targets the conditional intensity function through the notion of conditional Frechet means. We apply the method to study the effect of the temperature on the Chicago Divvy bike trips, the demand of yellow taxis according to the day of the week in New York as well as COVID-19 case and death point processes over countries depending on social distancing measures.