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Title: Testing a covariate dependent model for first-order intensity Authors:  Maria Isabel Borrajo - Universidade de Santiago de Compostela (Spain) [presenting]
Wenceslao Gonzalez-Manteiga - University of Santiago de Compostela (Spain)
Maria-Dolores Martinez-Miranda - Universidad de Granada (Spain)
Abstract: Modelling the first-order intensity function in one of the main aims in point process theory, and it has been approached so far from different perspectives. One appealing model describes the intensity as a function of a spatial covariate. In the recent literature, estimation theory and several applications have been developed assuming this hypothesis, but without formally checking the goodness-of-fit of the model. We address this problem and test whether the model is appropriate. We propose a test statistic based on a $L^2$-distance. We prove the asymptotic normality of the statistic and suggest a bootstrap procedure to calibrate the test. We present two applications with real data and a simulation study to better understand the performance of our proposals.