Bootstrapping kernel intensity estimation for inhomogeneous point processes with spatial covariates

Abstract

The bias-variance trade-o for inhomogeneous point processes with covariates is theoretically and empirically addressed. A consistent kernel estimator for the rst-order intensity function based on covariates is constructed, which uses a convenient relationship between the intensity and the density of events location. The asymptotic bias and variance of the estimator are derived and hence the expression of its infeasible optimal bandwidth. Three data-driven bandwidth selectors are proposed to estimate the optimal bandwidth. One of them is based on a new smooth bootstrap proposal which is proved to be consistent under a Poisson assumption. The other two are a rule-of-thumb method based on assuming normallity, and a simple non-model-based approach. An extensive simulation study is accomplished considering Poisson and non-Poisson scenarios, and including a comparison with other competitors. The practicality of the new proposals is shown through an application to real data about wild res in Canada, using meteorological covariates