CARTalgorithmforspatialdata:Applicationtoenvironmentaland ecologicaldata

a b s t r a c t Most statistical learning techniques such as Classification And Regression Trees (CART) assume independent samples to compute classification rules. This assumption is very practicalforestimatingquantitiesinvolvedinthealgorithmandforassessingasymptotic propertiesofestimators.Inmanyenvironmentalorecologicalapplications,thedataunder studyareasampleofsomeregionalizedvariables,whichcanbemodeledasrandomfields withspatialdependence.Whenthesamplingschemeisveryirregular,adirectapplication ofsupervisedclassificationalgorithmsleadstobiaseddiscriminantrulesdue,forexample, tothepossibleoversamplingofsomeareas.TheCARTalgorithmisadaptedtothecaseof spatiallydependentsamples,focusingonenvironmentalandecologicalapplications.Two approachesareconsidered.Thefirstonetakesintoaccounttheirregularityofthesampling byweightingthedataaccordingtotheirspatialpatternusingtwoexistingmethodsbased on VoronoO tessellation and regular grid, and one original method based on kriging. The second one uses spatial estimates of the quantities involved in the construction of the