Nonparametric inference on point processes with covariates

Abstract

Spatial statistics is a big area in the global statistical field which is interested in analysing any random process with a spatial component; point processes are a branch of spatial statistics whose main aim is to study the geometrical structure of patterns formed by objects (called events) that are distributed randomly in number and space. In this phD thesis, we provide with a consistent and well established theoretical framework in the field of point processes with covariates (extra information over the observation region given by a known spatially varying process), offering different innovative statistical methods in estimation and testing. We propose a new kernel intensity estimator, a resampling bootstrap method defined ad-hoc for this context as well as some specifically designed data-driven bandwidth selection procedures. We later use this to define and calibrate two statistical tests, the first one deciding if the covariate has influence on the process and the second letting us know if two intensity curves come from the same process. We also make a contribution in the field of density estimation for length-biased data with the detail of the theoretical characteristics of an existing kernel estimator, the definition of a new bootstrap method and two new data-driven bandwidth selectors. Moreover, all the methodology developed is analysed through several simulation studies and applications to real data sets.