Simple proof of the risk bound for denoising by exponential weights for asymmetric noise distributions

12/25/2022

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by   Arnak S. Dalalyan, et al.

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In this note, we consider the problem of aggregation of estimators in order to denoise a signal. The main contribution is a short proof of the fact that the exponentially weighted aggregate satisfies a sharp oracle inequality. While this result was already known for a wide class of symmetric noise distributions, the extension to asymmetric distributions presented in this note is new.