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Scale and Space Inference of NHPP Intensities

In this paper we develop the graphical exploratory tool Sizer Map for the intensity function of a nonhomogeneous Poisson process. SiZer Map is defined considering nonparametric local linear kernel estimators for the intensity function and its first derivative, where the bandwidth parameter is the viewing scale and the considered time interval is the localization space. The shape characteristics of the intensity function are distinguished from those which are merely an artifact of the sampling variability of the data through the construction of confidence intervals for the first derivative. The proposal is illustrated with several real datasets consisting of the occurrence times of events recurrent in time, and its performance is evaluated through an extensive simulation study.