最不利的噪音

IF 0.5 4区数学 Q4 STATISTICS & PROBABILITY

Electronic Communications in Probability Pub Date : 2021-03-17 DOI:10.1214/22-ecp467

Philip A. Ernst, A. Kagan, L. Rogers

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引用次数: 1

摘要

假设观察到感兴趣的随机变量X受到独立的加性噪声Y的扰动。本文讨论了在var（Y）≤ε的Y类中，使预测误差E（X−E（X|X+Y））2最大化的“最不有利扰动”。我们对这个问题的答案进行了描述，并通过例子表明它可能非常复杂。然而，在X是可整除的特殊情况下，解是完整而简单的。我们还探讨了噪声越大的Y使预测越差的猜想。

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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The least favorable noise

Suppose that a random variable X of interest is observed perturbed by independent additive noise Y . This paper concerns the “the least favorable perturbation” ˆ Y ε , which maximizes the prediction error E ( X − E ( X | X + Y )) 2 in the class of Y with var ( Y ) ≤ ε . We ﬁnd a characterization of the answer to this question, and show by example that it can be surprisingly complicated. However, in the special case where X is inﬁnitely divisible, the solution is complete and simple. We also explore the conjecture that noisier Y makes prediction worse.

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来源期刊

Electronic Communications in Probability 工程技术-统计学与概率论

CiteScore

1.00

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： The Electronic Communications in Probability (ECP) publishes short research articles in probability theory. Its sister journal, the Electronic Journal of Probability (EJP), publishes full-length articles in probability theory. Short papers, those less than 12 pages, should be submitted to ECP first. EJP and ECP share the same editorial board, but with different Editors in Chief.