Related papers: Assessing statistical significance of periodogram …
In this paper, an over-sampled periodogram higher criticism (OPHC) test is proposed for the global detection of sparse periodic effects in a complex-valued time series. An explicit minimax detection boundary is established between the…
We present an improvement of the phase distance correlation (PDC) periodogram to account for uncertainties in the time-series data. The PDC periodogram introduced in our previous papers is based on the statistical concept of distance…
The partial least squares procedure was originally developed to estimate the slope parameter in multivariate parametric models. More recently it has gained popularity in the functional data literature. There, the partial least squares…
We present new periodograms that are effective in distinguishing Doppler shift from spectral shape variability in astronomical spectra. These periodograms, building upon the concept of partial distance correlation, separate the periodic…
The detection of periodic signals in irregularly-sampled time series is a problem commonly encountered in astronomy. Traditional tools used for periodic searches, such as the periodogram, have poorly defined statistical properties under…
Astronomers who search for periodic signals using Lomb-Scargle periodograms rely on false alarm level (FAL) estimates to identify statistically significant peaks. Although FALs are often calculated from white noise models, many astronomical…
We carry out a comparative analysis of the performance of three algorithms widely used to identify significant periodicities in radial-velocity (RV) datasets: the Generalised Lomb-Scargle Periodogram (GLS), its modified version based on…
Nonlinear optimisation techniques are commonly employed to minimise complex cost functions, with their effectiveness determined largely by the structure of the underlying error landscape. These methods require initial parameter values, and…
Identifying frequencies with low signal-to-noise ratios in time series of stellar photometry and spectroscopy, and measuring their amplitude ratios and peak widths accurately, are critical goals for asteroseismology. These are also…
A method is presented for analysing over-determined sets of clock frequency comparison data involving standards based on a number of different reference transitions. This least-squares adjustment procedure, which is based on the method used…
We discuss different methods for phenomenological approximations of signals with (generally) irregularly spaced arguments. Such signals may be classified as periodic, multi-periodic, quasi-periodic (cyclic), burst-type and flicker-type (see…
The hunt for Earth analogue planets orbiting Sun-like stars has forced the introduction of novel methods to detect signals at, or below, the level of the intrinsic noise of the observations. We present a new global periodogram method that…
We address the problem of estimating the spherical-harmonic power spectrum of a statistically isotropic scalar signal from noise-contaminated data on a region of the unit sphere. Three different methods of spectral estimation are…
In experiments where one searches a large parameter space for an anomaly, one often finds many spurious noise-induced peaks in the likelihood. This is known as the look-elsewhere effect, and must be corrected for when performing statistical…
New time-series analysis tools are needed in disciplines as diverse as astronomy, economics and meteorology. In particular, the increasing rate of data collection at multiple wavelengths requires new approaches able to handle these data.…
Quasi-periodic modulations of the stellar light curve may result from dark spots crossing the visible stellar disc. Due to differential rotation, spots at different latitudes generally have different rotation periods. Hence, by studying…
Feature importance scores are ubiquitous tools for understanding the predictions of machine learning models. However, many popular attribution methods suffer from high instability due to random sampling. Leveraging novel ideas from…
In this paper, we explain a procedure based on a classical result of Sturm that can be used to determine rigorously whether a given trigonometric polynomial is nonnegative in a certain interval or not. Many examples are given. This…
The sensitivities of two periodograms are compared for weak signal planet detection in transit surveys: the widely used Box-Least Squares (BLS) algorithm following light curve detrending and the Transit Comb Filter (TCF) algorithm following…
A weighted regression procedure is proposed for regression type problems where the innovations are heavy-tailed. This method approximates the least absolute regression method in large samples, and the main advantage will be if the sample is…