A Novel Tree Ensemble Model to Approximate the Generalized Extreme Value Distribution Parameters of the PM2.5 Maxima in the Mexico City Metropolitan Area

Abstract

We introduce a novel spatial model based on the distribution of generalized extreme values (GEVs) and tree ensemble models to analyze the maximum concentrations levels of particulate matter with a diameter of less than 2.5 microns (PM2.5) in the Mexico City metropolitan area during the period 2003–2021. Spatial trends were modeled through a decision tree in the context of a non-stationary GEV model. We used a tree ensemble model as a predictor of GEV parameters to approximate nonlinear trends. The decision tree was built by using a greedy stagewise approach, the objective function of which was the log-likelihood. We verified the validity of our model by means of the likelihood and Akaike’s information criterion (AIC). The maps of the generalized extreme value parameters on the spatial plane show the existence of differentiated local trends in the extreme values of PM2.5 in the study area. The results indicated strong evidence of an increase in the west–east direction of the study area. A spatial map of risk with maximum concentration levels of PM2.5 in a period of 25 years was built.