Robust statistical signal processing in semi-Markov nonparametric regression models

International audienceWe develop model sélection methods for robust processing of nonparametric periodic signais observed in continuons time with noises containing impulse components defined by a non Gaussian semi - Markov processes. In particular, we apply the developed model sélection methods for the détection problem of the number of signais in multi-path information transmission observed with complex dépendent impulse semi-Markov noises. As an example of semi-Markov noises, we consider the signais models with the noises defined through fractional Poisson processes. For this problem we show non asymptotic sharp oracle inequalities for robust risks, i.e., we show that the constructed procedures are optimal in the sense of sharp oracle inequalities