Related papers: Testing for high frequency features in a noisy sig…
Functional Principal Component Analysis is a reference method for dimension reduction of curve data. Its theoretical properties are now well understood in the simplified case where the sample curves are fully observed without noise.…
It is by now established that, remarkably, the addition of noise to a nonlinear system may sometimes facilitate, rather than hamper the detection of weak signals. This phenomenon, usually referred to as stochastic resonance, was originally…
Estimating signals underlying noisy data is a significant problem in statistics and engineering. Numerous estimators are available in the literature, depending on the observation model and estimation criterion. This paper introduces a…
A parameter estimation problem is considered for a diagonaliazable stochastic evolution equation using a finite number of the Fourier coefficients of the solution. The equation is driven by additive noise that is white in space and…
Quantitative helio- and asteroseismology require very precise measurements of the frequencies, amplitudes, and lifetimes of the global modes of stellar oscillation. It is common knowledge that the precision of these measurements depends on…
As our ability to sense increases, we are experiencing a transition from data-poor problems, in which the central issue is a lack of relevant data, to data-rich problems, in which the central issue is to identify a few relevant features in…
We describe a statistical hypothesis test for the presence of a signal. The test allows the researcher to fix the signal location and/or width a priori, or perform a search to find the signal region that maximizes the signal. The background…
We consider problem of signal detection in Gaussian white noise. Test statistics are linear combinations of squares of estimators of Fourier coefficients or $\mathbb{L}_2$-norms of kernel estimators. We point out necessary and sufficient…
In this paper, a new statistic feature of the discrete short-time amplitude spectrum is discovered by experiments for the signals of unvoiced pronunciation. For the random-varying short-time spectrum, this feature reveals the relationship…
We present and analyze the simple analytically solvable model of 1/f noise, which can be relevant for the understanding of the origin, main properties and parameter dependencies of the flicker noise. In the model, the currents or signals…
The frequency response function (FRF) is a typical way to describe the outcome of experiments where posture control is perturbed with an external stimulus. The FRF is an empirical transfer function between an input stimulus and the induced…
Analytical understanding of how low-dimensional latent features reveal themselves in large-dimensional data is still lacking. We study this by defining a linear latent feature model with additive noise constructed from probabilistic…
We propose a new test statistic based on a score process for determining the statistical significance of a putative signal that may be a small perturbation to a noisy experimental background. We derive the reference distribution for this…
Rock properties are environment- and condition-dependent which render field-laboratory comparisons ambiguous for a number of known and unknown reasons that constitute the upscaling problem. Unknowns are first transformed into knowns in a…
Interest in functional time series has spiked in the recent past with papers covering both methodology and applications being published at a much increased pace. This article contributes to the research in this area by proposing a new…
This paper studies different signaling techniques on the continuous spectrum (CS) of nonlinear optical fiber defined by nonlinear Fourier transform. Three different signaling techniques are proposed and analyzed based on the statistics of…
Accelerometry data has been widely used to measure activity and the circadian rhythm of individuals across the health sciences, in particular with people with advanced dementia. Modern accelerometers can record continuous observations on a…
A method is developed for analysing asymptotic behaviour of terms involving an arbitrary integer order powers of L p functions by means of H-measures. It is applied to the small amplitude homogenisation problem for a stationary diffusion…
Noisy vibrotactile signals transmitted during tactile explorations of an object provide precious information on the nature of its surface. Linking the properties of such vibrotactile signals to the way they are interpreted by the haptic…
Nearly all identifiability results in unsupervised representation learning inspired by, e.g., independent component analysis, factor analysis, and causal representation learning, rely on assumptions of additive independent noise or…