Related papers: Generalized Mode and Ridge Estimation
In this work we derive an inversion formula for the Laplace transform of a density observed on a curve in the complex domain, which generalizes the well known Post-Widder formula. We establish convergence of our inversion method and derive…
Clusters of galaxies are important laboratories for understanding both galaxy evolution and constraining cosmological quantities. Any analysis of clusters, however, is best done when one can reliably determine which galaxies are members of…
Density level sets can be estimated using plug-in methods, excess mass algorithms or a hybrid of the two previous methodologies. The plug-in algorithms are based on replacing the unknown density by some nonparametric estimator, usually the…
In this paper we provide new methodology for inference of the geometric features of a multivariate density in deconvolution. Our approach is based on multiscale tests to detect significant directional derivatives of the unknown density at…
Generalized dimensions of multifractal measures are usually seen as static objects, related to the scaling properties of suitable partition functions, or moments of measures of cells. When these measures are invariant for the flow of a…
A generalization of Gy's theory for the variance of the fundamental sampling error is reviewed. Practical situations where the generalized model potentially leads to more accurate variance estimates are identified as: clustering of…
The directional mean shift (DMS) algorithm is a nonparametric method for pursuing local modes of densities defined by kernel density estimators on the unit hypersphere. In this paper, we show that any DMS iteration can be viewed as a…
We construct a consistency test of General Relativity (GR) on cosmological scales. This test enables us to distinguish between the two alternatives to explain the late-time accelerated expansion of the universe, that is, dark energy models…
We have worked out simple analytical formulae that accurately approximate the relationship between the position of the source with respect to the lens center and the amplification of the images, hence the lens cross section, for realistic…
We use Stein's method to obtain bounds on the rate of convergence for a class of statistics in geometric probability obtained as a sum of contributions from Poisson points which are exponentially stabilizing, i.e. locally determined in a…
Probability density estimation is a classical and well studied problem, but standard density estimation methods have historically lacked the power to model complex and high-dimensional image distributions. More recent generative models…
This paper develops a density deconvolution estimator that assumes the density of interest is a member of the generalized skew-symmetric (GSS) family of distributions. Estimation occurs in two parts: a skewing function, as well as location…
Our view of the properties of galaxies is strongly affected by the way in which we survey for them. I discuss some aspects of selection effects and methods to compensate for them. One result is an estimate of the surface brightness…
Joint lensing and dynamical mass profile determinations of galaxy clusters are an excellent tool to constrain modification of gravity at cosmological scales. However, search for tiny departures from General Relativity calls for an accurate…
The different regimes of gravitational lensing constitutes an interesting tool in order to map the mass distribution in galaxy clusters on different scales. In this proceedings article, I review some work I have performed on this topic.…
Context: The number of known strong gravitational lenses is expected to grow substantially in the next few years. The statistical combination of large samples of lenses has the potential of providing strong constraints on the inner…
Density ratio estimation serves as an important technique in the unsupervised machine learning toolbox. However, such ratios are difficult to estimate for complex, high-dimensional data, particularly when the densities of interest are…
Measurements of the luminosity distance of propagating gravitational waves can provide invaluable information on the geometry and content of our Universe. Due to the clustering of cosmic structures, in realistic situations we need to…
The aim of this paper is to identify and study the properties and galactic content of groups and clusters in the GOODS-South field up to z\sim2.5, and to analyse the physical properties of galaxies as a continuous function of environmental…
We study moderate gravitational lensing where a background galaxy is magnified substantially, but not multiply imaged, by an intervening galaxy. We focus on the case where both the lens and source are elliptical galaxies. The signatures of…