Cox Point Process Regression

Point processes in time have a wide range of applications that include the claims arrival process insurance or analysis queues operations research. Due to advances technology, such samples point are increasingly encountered. A key object interest is local intensity function. It has straightforward interpretation allows understand and explore data. We consider functional approaches for processes, where one sample repeated realizations process. This situation inherently connected with Cox functions replications modeled as random functions. Here we study records covariates each replication process, daily temperature bike rentals. For modeling responses vector predictors propose novel regression approach function intrinsically nonparametric. While only observed once on fixed domain cannot be identified, show how observations can utilized make consistent estimation possible, also derive asymptotic rates convergence without invoking parametric assumptions.