Risk with random normalizing factors in the white gaussian noise additive model
Résumé
In the context of minimax theory we develop a new approach based on pretesting. The first step of this approach consists in testing some structural assumption imposed on the underlying function. According to the result we use a relevant estimation procedure that allows to improve significantly the quality of estimation. We apply this general set-up to the estimation of an unknown multidimensional signal in the White Gaussian Noise model. The structure we test here is the additivity hypothesis. The mathematical description of this approach leads to the notion of random (depending on datas) rate of estimation. Under some additional assumption our construction leads to adaptive estimator w.r.t. rate of convergence.
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