Related papers: On More Sensitive Periodogram Statistics
Interferometric measurements of high-harmonics induced by multiple laser fields in an emerging field of research that promises optimized yield of harmonics, and time and space-resolved nonlinear spectroscopy. Most of the measurements have…
We use Legendre polynomials, previously employed in this context by Lee et al., van Haasteren and Levin, and Pitrou and Cusin, to model signals in pulsar timing arrays. These replace the (Fourier mode) basis of trigonometric functions…
Thermoacoustic instabilities are one of the most challenging problems faced by gas turbine and rocket motor manufacturers. The key instability mechanism is described by the {\it Rayleigh criterion}. The Rayleigh criterion does not directly…
The periodogram is a widely used tool to analyze second order stationary time series. An attractive feature of the periodogram is that the expectation of the periodogram is approximately equal to the underlying spectral density of the time…
For many relevant statistics of multivariate time series, no valid frequency domain bootstrap procedures exist. This is mainly due to the fact that the distribution of such statistics depends on the fourth-order moment structure of the…
The detection of pulsations from an X-ray binary is an unambiguous signature of the presence of a neutron star in the system. When the pulsations are missed in the radio band, their detection at other wavelengths, like X-ray or gamma-rays,…
The Rayleigh criterion is a widely known limit in the resolution of incoherent sources with classical measurements in the spatial domain. Unsurprisingly the estimation of the time delay between two weak incoherent signals is afflicted by an…
Searching for combinations in the frequency spectra of variable stars is a commonly used method within the asteroseismological community, as harmonics and linear combinations of individual frequencies are expected to appear not only by…
We present a mathematical analysis of the statistical parallax method. The method yields physical insight into the maximum-likelihood determinations of the luminosity and velocity distribution and enables us to conduct a vigorous Monte…
In the matter of selection of sample time points for the estimation of the power spectral density of a continuous time stationary stochastic process, irregular sampling schemes such as Poisson sampling are often preferred over regular…
Spectral and temporal coincidence and single-particle photon wave packets are described and their widths and durations are found. The degree of entanglement is characterized by the experimentally measurable parameter R defined as the ratio…
We are interested to detect periodic signals in Hilbert space valued time series when the length of the period is unknown. A natural test statistic is the maximum Hilbert-Schmidt norm of the periodogram operator over all fundamental…
The purpose of this study is to provide a new methodology of how one can consistently estimate a change-point in time series data. In contrast with previous studies, the suggested methodology employs only the empirical spectral density and…
The ubiquity of integrating detectors in imaging and other applications implies that a variety of real-world data are well modeled as Poisson random variables whose means are in turn proportional to an underlying vector-valued signal of…
Double-mode RR Lyrae variables (i.e. radial variables which are simultaneously pulsating in both fundamental and first overtone modes) appear a fundamental tool for investigating the mass of old Population II Horizontal Branch (HB) stars.…
The robust detection of statistical dependencies between the components of a complex system is a key step in gaining a network-based understanding of the system. Because of their simplicity and low computation cost, pairwise statistics are…
Astrophysical time series often contain periodic signals. The large and growing volume of time series data from photometric surveys demands computationally efficient methods for detecting and characterizing such signals. The most efficient…
The averaging method is a classical powerful tool in perturbation theory of dynamical systems. There are two major obstacles to applying the averaging method, resonances and separatrices. In this paper we obtain realistic asymptotic…
We analyse the stochastic properties of the 49 pulsars that comprise the first International Pulsar Timing Array (IPTA) data release. We use Bayesian methodology, performing model selection to determine the optimal description of the…
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…