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Abstract: In this paper, we deal with the problem of calibrating thresholding rules inthe setting of Poisson intensity estimation. By using sharp concentrationinequalities, oracle inequalities are derived and we establish the optimalityof our estimate up to a logarithmic term. This result is proved under mildassumptions and we do not impose any condition on the support of the signal tobe estimated. Our procedure is based on data-driven thresholds. As usual, theydepend on a threshold parameter $\gamma$ whose optimal value is hard toestimate from the data. Our main concern is to provide some theoretical andnumerical results to handle this issue. In particular, we establish theexistence of a minimal threshold parameter from the theoretical point of view:taking $\gamma<1$ deteriorates oracle performances of our procedure. In thesame spirit, we establish the existence of a maximal threshold parameter andour theoretical results point out the optimal range $\gamma\in1,12$. Then, welead a numerical study that shows that choosing $\gamma$ larger than 1 butclose to 1 is a fairly good choice. Finally, we compare our procedure withclassical ones revealing the harmful role of the support of functions whenestimated by classical procedures.



Autor: Patricia Reynaud-Bouret, Vincent Rivoirard

Fuente: https://arxiv.org/







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