Signal-to-noise ratio (SNR) statistics play a central role in many applications. A common situation where SNR is studied is when a continuous time signal is sampled at a fixed frequency with some noise in the background. While estimation methods exist, little is known about its distribution when the noise is not weakly stationary. In this paper we develop a nonparametric method to estimate the distribution of an SNR statistic when the noise belongs to a fairly general class of stochastic processes that encompasses both short and long-range dependence, as well as nonlinearities. The method is based on a combination of smoothing and subsampling techniques. Computations are only operated at the subsample level, and this allows to manage the typical enormous sample size produced by modern data acquisition technologies. We derive asymptotic guarantees for the proposed method, and we show the finite sample performance based on numerical experiments. Finally, we propose an application to electroencephalography (EEG) data.
翻译:信号对噪音比率(SNR)统计在许多应用中发挥着核心作用。研究SNR的一个常见情况是连续时间信号以固定频率取样,在背景中有一些噪音。虽然存在估计方法,但在噪音不固定的情况下,对信号的分布情况知之甚少。在本文中,我们开发了一种非参数方法,用以估计SNR统计数据的分布情况,当噪音属于相当一般的一类随机过程,包括短长的依赖性和非线性。这种方法基于平滑和子取样技术的结合。计算只在次抽样层进行,从而能够管理现代数据采集技术产生的典型巨大样本规模。我们从中得出对拟议方法的无保障,我们根据数字实验展示有限的样本性能。最后,我们提议对电子脑学数据进行应用。