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The paper considers the stationary Poisson Boolean model with spherical grains and proposes a family of nonparametric estimators for the radius distribution. These estimators are based on observed distances and radii, weighted in an…
Covariance parameter estimation of Gaussian processes is analyzed in an asymptotic framework. The spatial sampling is a randomly perturbed regular grid and its deviation from the perfect regular grid is controlled by a single scalar…
It is proposed a class of statistical estimators $\hat H =(\hat H_1, \ldots, \hat H_d)$ for the Hurst parameters $H=(H_1, \ldots, H_d)$ of fractional Brownian field via multi-dimensional wavelet analysis and least squares, which are…
Cosmological parameter uncertainties are often stated assuming a particular model, neglecting the model uncertainty, even when Bayesian model selection is unable to identify a conclusive best model. Bayesian model averaging is a method for…
We develop two methods for estimating the power spectrum, C_l, of the cosmic microwave background (CMB) from data and apply them to the COBE/DMR and Saskatoon datasets. One method involves a direct evaluation of the likelihood function, and…
This paper is concerned with density estimation of directional data on the sphere. We introduce a procedure based on thresholding on a new type of spherical wavelets called {\it needlets}. We establish a minimax result and prove its…
We study the estimation of quadratic Sobolev-type integral functionals of an unknown density on the unit sphere. The functional is defined through fractional powers of the Laplace--Beltrami operator and provides a global measure of…
In a previous paper (part I), the mathematical properties of the cosmic microwave background radiation power spectrum which presents oscillations were discussed. Here, we discuss the physical interpretation: a power spectrum with…
The nonlinear parameter measures the amplitude of primordial non-Gaussianity in the cosmic microwave background radiation (CMB), offering a crucial test of early universe models. While standard single field inflation predicts nearly…
Physicists routinely need probabilistic models for a number of tasks such as parameter inference or the generation of new realizations of a field. Establishing such models for highly non-Gaussian fields is a challenge, especially when the…
The noise of a device under test (DUT) is measured simultaneously with two instruments, each of which contributes its own background. The average cross power spectral density converges to the DUT power spectral density. This method enables…
In principle the geometry of the universe can be investigated by measuring the angular size of known objects as a function of distance. Thus the distribution of angular sizes provides a critical test of the stable and static model of the…
The density function of the limiting spectral distribution of general sample covariance matrices is usually unknown. We propose to use kernel estimators which are proved to be consistent. A simulation study is also conducted to show the…
In this paper we deal with the problem of predicting a steady-state neutron spectrum in media of arbitrary composition and geometry. The analytical calculations of such spectrum are often too complex, if at all possible. We describe a…
Galactic synchrotron and free-free foregrounds angular spectra are analytically estimated with account for interstellar turbulence and radiating process physics. Unknown parameters of the spectra are obtained by fitting to observational…
We consider the multi-frequency inverse source problem in the presence of a non-homogeneous medium using passive measurements. Precisely, we derive stability estimates for determining the source from the knowledge of only the imaginary part…
Spectral components of continuous squeezed fields are entangled. In this article we review and clarify this phenomenon by analyzing systematically the relations between the correlations of modes filtered from stationary continuous fields…
We discuss the derivation of the analytic properties of the cross-power spectrum estimator from multi-detector CMB anisotropy maps. The method is computationally convenient and it provides unbiased estimates under very broad assumptions. We…
We present a formalism to extract the angular power spectrum of fields sampled at a finite number of points with arbitrary positions -- a common situation for several catalog-based astrophysical probes -- through a simple extension of the…
Cosmological theories for the origin and evolution of structure in the Universe are highly predictive of the form of the angular power spectrum of cosmic microwave background fluctuations. We present new results from a comprehensive study…