Penalized Projection Estimators of the Aalen Multiplicative Intensity
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We study the problem of non parametric estimation of the intensity of counting processes satisfying the Aalen multiplicative intensity model. To do so, we use model selection techniques and more precisely penalized projection estimators for a random inner product. For histogram estimators, under some assumptions on the process, we obtain adaptive results for the minimax risk. In general, for more intricate (predictable) models, we only obtain oracle inequalities. The study is completed by some simulations in the right-censoring model.