  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.
