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The nonparametric estimation of the volatility and the drift coefficient of a scalar diffusion is studied when the process is observed at random time points. The constructed estimator generalizes the spectral method by Gobet, Hoffmann and…
A dynamical scalar field represents the simplest generalization of a pure Cosmological Constant as a candidate to explain the recent evidence in favour of the accelerated cosmic expansion. We review the dynamical properties of such a…
Unresolved and resolved sources of gravitational waves are at the origin of a stochastic gravitational wave background. While the computation of its mean density as a function of frequency in a homogeneous and isotropic universe is standard…
A new multivariate density estimator for stationary sequences is obtained by Fourier inversion of the thresholded empirical characteristic function. This estimator does not depend on the choice of parameters related to the smoothness of the…
The power spectrum of mass density fluctuations is evaluated from the Mark III and the SFI catalogs of peculiar velocities by a maximum likelihood analysis, using parametric models for the power spectrum and for the errors. The applications…
In this paper we establish a multiscale approximation for random fields on the sphere using spherical needlets --- a class of spherical wavelets. We prove that the semidiscrete needlet decomposition converges in mean and pointwise senses…
A method to extract primary $\gamma$-ray spectra from particle-$\gamma$ coincidences at excitation energies up to the neutron binding energy is described. From these spectra, the level density and $\gamma$-ray strength function can be…
We use the techniques developed in [1] to study the local average of random fields with spectral density $1/f^{\alpha}$. We study their scaling properties and show that the self-similarity of $1/f$ random fields is preserved under the local…
A method is developed for fitting theoretically predicted astronomical spectra to an observed spectrum. Using a hierarchical Bayesian principle, the method takes both systematic and statistical measurement errors into account, which has not…
Cosmic shear tomography has emerged as one of the most promising tools to both investigate the nature of dark energy and discriminate between General Relativity and modified gravity theories. In order to successfully achieve these goals,…
We use an iterative generalized least squares map-making algorithm, in conjunction with Monte Carlo techniques, to obtain estimates of the angular power spectrum from cosmic microwave background (CMB) maps. This is achieved by…
An efficient technique for computing perturbation power spectra in field ordering theories of cosmic structure formation is introduced, enabling computations to be carried out with unprecedented precision. Large scale simulations are used…
Regression on observational data can fail to capture a causal relationship in the presence of unobserved confounding. Confounding strength measures this mismatch, but estimating it requires itself additional assumptions. A common assumption…
A parameter estimation problem is considered for a one-dimensional stochastic wave equation driven by additive space-time Gaussian white noise. The estimator is of spectral type and utilizes a finite number of the spatial Fourier…
The cosmological power spectrum of the coherent matter flow is measured exploiting an improved prescription for the apparent anisotropic clustering pattern in redshift space. New statistical analysis is presented to provide an optimal…
Angular power spectrum of the cosmic microwave background (CMB) temperature anisotropies is one of the most important on characteristics of the Universe such as its geometry and total density. Using flat sky approximation and Fourier…
The sensitivity of gravitational-wave (GW) detectors is characterized by their noise curves, which determine the detector's reach and ability to measure the parameters of astrophysical sources accurately. The detector noise is typically…
We consider the correlation structure of the random coefficients for a wide class of wavelet systems on the sphere (Mexican needlets) which were recently introduced in the literature by Geller and Mayeli (2007). We provide necessary and…
We develop a method to estimate the power spectrum of a stochastic process on the sphere from data of limited geographical coverage. Our approach can be interpreted either as estimating the global power spectrum of a stationary process when…
Scale-discretised wavelets yield a directional wavelet framework on the sphere where a signal can be probed not only in scale and position but also in orientation. Furthermore, a signal can be synthesised from its wavelet coefficients…