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This paper deals with a non-parametric problem coming from physics, namely quantum tomography. That consists in determining the quantum
state of a mode of light through a homodyne measurement. We
apply several model selection procedures: penalized projection estimators,
where we may use pattern functions or wavelets, and penalized maximum
likelihood estimators. In all these cases, we get oracle inequalities. In the
former we also have a polynomial rate of convergence for the non-parametric
problem....
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