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

TL;DR

This paper provides a concise proof that exponentially weighted aggregation achieves a sharp oracle inequality for denoising signals, extending known results from symmetric to asymmetric noise distributions.

Contribution

It offers the first proof of the risk bound for exponential weights in denoising with asymmetric noise distributions.

Findings

Exponential weights satisfy a sharp oracle inequality for asymmetric noise.

The proof extends previous results from symmetric to asymmetric noise.

The result broadens the applicability of aggregation methods in signal denoising.

Abstract

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.