非对称噪声分布的指数加权去噪风险边界的简单证明

IF 0.3 4区数学 Q4 MATHEMATICS

Journal of Contemporary Mathematical Analysis-Armenian Academy of Sciences Pub Date : 2023-12-28 DOI:10.3103/s106836232306002x

A. S. Dalalyan

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引用次数: 0

摘要

摘要在本说明中，我们考虑了为对信号进行去噪而聚合估计子的问题。它的主要贡献在于简短地证明了指数加权集合满足一个尖锐的甲骨文不等式。虽然这一结果在许多对称噪声分布中已为人所知，但本论文将其扩展到非对称分布则是一个新发现。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Simple Proof of the Risk Bound for Denoising by Exponential Weights for Asymmetric Noise Distributions

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.

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来源期刊

Journal of Contemporary Mathematical Analysis-Armenian Academy of Sciences MATHEMATICS-

CiteScore

0.70

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences) is an outlet for research stemming from the widely acclaimed Armenian school of theory of functions, this journal today continues the traditions of that school in the area of general analysis. A very prolific group of mathematicians in Yerevan contribute to this leading mathematics journal in the following fields: real and complex analysis; approximations; boundary value problems; integral and stochastic geometry; differential equations; probability; integral equations; algebra.