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An estimation approach for the semi-parametric intensity function of a class of space-time point processes is introduced. In particular we want to account for the estimation of parametric and nonparametric components simultaneously, applying a forward predictive likelihood to semi-parametric models. For each event, the probability of being a background event or an offspring is therefore estimated.

Erratum to: Alternated estimation in semi-parametric space-time branching-type point processes with application to seismic catalogs