Related papers: FINKER: Frequency Identification through Nonparame…

Time stretch instruments have been exceptionally successful in discovering single-shot ultrafast phenomena such as optical rogue waves and have led to record-speed microscopy, spectroscopy, lidar, etc. These instruments encode the ultrafast…

The ability to automatically and robustly self-verify periodicity present in time-series astronomical data is becoming more important as data sets rapidly increase in size. The age of large astronomical surveys has rendered manual…

Time-frequency analysis is an important and challenging task in many applications. Fourier and wavelet analysis are two classic methods that have achieved remarkable success in many fields. However, they also exhibit limitations when…

Statistical modeling of experimental physical laws is based on the probability density function of measured variables. It is expressed by experimental data via a kernel estimator. The kernel is determined objectively by the scattering of…

Since many decades, there is a general perception in literature that the Fourier methods are not suitable for the analysis of nonlinear and nonstationary data. In this paper, we propose a Fourier Decomposition Method (FDM) and demonstrate…

Context. Filamentary structures appear to be ubiquitous in the interstellar medium. Being able to detect and characterize them is the first step toward understanding their origin, their evolution, and their role in the Galactic cycle of…

We consider the prediction problem of a continuous-time stochastic process on an entire time-interval in terms of its recent past. The approach we adopt is based on functional kernel nonparametric regression estimation techniques where…

The Fourier spectrum at a fractional period is often examined when extracting features from biological sequences and time series. It reflects the inner information structure of the sequences. A fractional period is not uncommon in time…

This paper develops empirical likelihood methodology for irregularly spaced spatial data in the frequency domain. Unlike the frequency domain empirical likelihood (FDEL) methodology for time series (on a regular grid), the formulation of…

Telescopes are much more expensive than astronomers, so it is essential to minimize required sample sizes by using the most data-efficient statistical methods possible. However, the most commonly used model-independent techniques for…

In this paper we present a multiresolution-based method for period determination that is able to deal with unevenly sampled data. This method allows us to detect superimposed periodic signals with lower signal-to-noise ratios than in…

E-science of photometric data requires automatic procedures and a precise recognition of periodic patterns to perform science as well as possible on large data. Analytical equations that enable us to set the best constraints to properly…

This work explores new classes of nonstationary stochastic sequences associated with polynomial hypergroups. Their covariance structures are analyzed through positive definite kernels and corresponding Hilbert spaces. Novel consistent…

A class of methods for measuring time delays between astronomical time series is introduced in the context of quasar reverberation mapping, which is based on measures of randomness or complexity of the data. Several distinct statistical…

Context. Solar-like oscillations exhibit a regular pattern of frequencies. This pattern is dominated by the small and large frequency separations between modes. The accurate determination of these parameters is of great interest, because…

Accurately measuring stellar ages and internal structures is challenging, but the inclusion of asteroseismic observables can substantially improve precision. However, the curse of dimensionality means this comes at a high computational cost…

We propose non-stationary spectral kernels for Gaussian process regression. We propose to model the spectral density of a non-stationary kernel function as a mixture of input-dependent Gaussian process frequency density surfaces. We solve…

Recent normalization-based methods have shown great success in tackling the distribution shift issue, facilitating non-stationary time series forecasting. Since these methods operate in the time domain, they may fail to fully capture the…

We consider the problem of making nonparametric inference in a class of multi-dimensional diffusions in divergence form, from low-frequency data. Statistical analysis in this setting is notoriously challenging due to the intractability of…

In this paper, we show that the presence of nonlinear coupling between time series may be detected employing kernel feature space representations alone dispensing with the need to go back to solve the pre-image problem to gauge model…