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In this paper, we consider the detection of a small change in the frequency of sinusoidal signals, which arises in various signal processing applications. The generalized likelihood ratio test (GLRT) for this problem uses the maximum…
We consider the problem of detecting deviations from a white noise assumption in time series. Our approach differs from the numerous methods proposed for this purpose with respect to two aspects. First, we allow for non-stationary time…
Common techniques in Gravitational Wave data analysis assume, to some extent, the stationarity and Gaussianity of the detector noise. These assumptions are not always satisfied because of the presence of short-duration transients, namely…
The output of gravitational-wave interferometers, such as LIGO and Virgo, can be highly non-stationary. Broadband detector noise can affect the detector sensitivity on the order of tens of seconds. Gravitational-wave transient searches,…
Spectrum sensing is a crucial component of opportunistic spectrum access schemes, which aim at improving spectrum utilization by allowing for the reuse of idle licensed spectrum. Sensing a spectral band before using it makes sure the…
In real-world problems, environmental noise is often idealized as Gaussian white noise, despite potential temporal dependencies. The Linear Inverse Model (LIM) is a class of data-driven methods that extract dynamic and stochastic…
We consider multi-antenna cooperative spectrum sensing in cognitive radio networks, when there may be multiple primary users. A noise-uncertainty-free detector that is optimal in the low signal to noise ratio regime is analyzed in such a…
We derive several tests for the presence of a periodic component in a time series of functions. We consider both the traditional setting in which the periodic functional signal is contaminated by functional white noise, and a more general…
Some systems cannot be predicted by classical theories and it is required the development of combined deterministic and stochastic theories that make used of noise for dynamical prediction. Noise is not always an interfering signal which…
A generic `chirp' of the form h(t) = A(t) cos(phi(t)) can be closely approximated by a connected set of multiscale chirplets with quadratically-evolving phase. The problem of finding the best approximation to a given signal using chirplets…
This paper considers the problem of detecting nonstationary phenomena, and chirps in particular, from very noisy data. Chirps are waveforms of the very general form A(t) exp(i\lambda \phi(t)), where \lambda is a (large) base frequency, the…
We propose a new procedure for white noise testing of a functional time series. Our approach is based on an explicit representation of the $L^2$-distance between the spectral density operator and its best ($L^2$-)approximation by a spectral…
Signal detection in colored noise with an unknown covariance matrix has a myriad of applications in diverse scientific/engineering fields. The test statistic is the largest generalized eigenvalue (l.g.e.) of the whitened sample covariance…
We consider the problem of sequential binary hypothesis testing with a distributed sensor network in a non-Gaussian noise environment. To this end, we present a general formulation of the Consensus + Innovations Sequential Probability Ratio…
Signal detection in environments with unknown signal bandwidth and time intervals is a fundamental problem in adversarial and spectrum-sharing scenarios. This paper addresses the problem of detecting signals occupying unknown degrees of…
In supervised learning, automatically assessing the quality of the labels before any learning takes place remains an open research question. In certain particular cases, hypothesis testing procedures have been proposed to assess whether a…
In this paper we propose a nonparametric procedure for validating the assumption of stationarity in multivariate locally stationary time series models. We develop a bootstrap assisted test based on a Kolmogorov-Smirnov type statistic, which…
The ability to characterize the state of dynamic systems has been a pertinent task in the time series analysis community. Traditional measures such as Lyapunov exponents are often times difficult to recover from noisy data, especially if…
Detecting conditional independencies plays a key role in several statistical and machine learning tasks, especially in causal discovery algorithms. In this study, we introduce LCIT (Latent representation based Conditional Independence…
The local, uncorrelated multiplicative noises driving a second-order, purely noise-induced, ordering phase transition (NIPT) were assumed to be Gaussian and white in the model of [Phys. Rev. Lett. \textbf{73}, 3395 (1994)]. The potential…