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We have derived accurate distances to Galactic globular clusters by combining data from the Gaia Early Data Release 3 with distances based on Hubble Space telescope HST data and literature based distances. We determine distances either…
This paper is concerned with the Stein's method associated with a (possibly) asymmetric $\alpha$-stable distribution $Z$, in dimension one. More precisely, its goal is twofold. In the first part, we exhibit a genuine bound for the…
In this paper we outline the framework of mathematical statistics with which one may study the properties of galaxy distance estimators. We describe, within this framework, how one may formulate the problem of distance estimation as a…
The second Gaia data release (GDR2) provides precise five-parameter astrometric data (positions, proper motions and parallaxes) for an unprecedented amount of sources (more than $1.3$ billion, mostly stars). The use of this wealth of…
We present here a method to study the distribution of electron density fluctuations in pulsar directions as well as to estimate pulsar distances. The method, based on a simple two-component model of the scattering medium discussed by Gwinn…
Estimating a distance by inverting a parallax is only valid in the absence of noise. As most stars in the Gaia catalogue will have non-negligible fractional parallax errors, we must treat distance estimation as a constrained inference…
We consider the problem of allocating samples to a finite set of discrete distributions in order to learn them uniformly well in terms of four common distance measures: $\ell_2^2$, $\ell_1$, $f$-divergence, and separation distance. To…
Lutz & Kelker showed that parallax measurements are systematically overestimated because they do not properly account for the larger volume of space that is sampled at smaller parallax values. We apply their analysis to neutron stars,…
Like Hipparcos, Gaia is designed to give absolute parallaxes, independent of any astrophysical reference system. And indeed, Gaia's internal zero-point error for parallaxes is likely to be smaller than any individual parallax error.…
An extension of the Gauss-Newton algorithm is proposed to find local minimizers of penalized nonlinear least squares problems, under generalized Lipschitz assumptions. Convergence results of local type are obtained, as well as an estimate…
Context. Currently galactic exploration is being revolutionized by a flow of new data: Gaia provides measurements of stellar distances and kinematics; growing numbers of spectroscopic surveys provide values of stellar atmospheric parameters…
We establish quantitative comparisons between classical distances for probability distributions belonging to the class of convex probability measures. Distances include total variation distance, Wasserstein distance, Kullback-Leibler…
Hipparcos parallaxes fix distances to individual stars in the Hyades cluster with an accuracy of 6%. We use the Hipparcos (and Tycho-2) proper motions, which have a larger relative precision than the trigonometric parallaxes, to derive ~3…
We present a new method for detecting and correcting systematic errors in the distances to stars when both proper motions and line-of-sight velocities are available. The method, which is applicable for samples of 200 or more stars that have…
We develop a unified approach for establishing rates of decay for the Fourier transform of a wide class of dynamically defined measures. Among the key features of the method is the systematic use of the $L^2$-flattening theorem obtained in…
Aims: We provide a new distance estimate for the Pleiades based on the moving cluster method, which will be useful to further discuss the so-called Pleiades distance controversy and compare it with the very precise parallaxes from the Gaia…
In this paper, we study the strong consistency of the sparse K-means clustering for high dimensional data. We prove the consistency in both risk and clustering for the Euclidean distance. We discuss the characterization of the limit of the…
I describe a Bayesian method to account for measurement errors in linear regression of astronomical data. The method allows for heteroscedastic and possibly correlated measurement errors, and intrinsic scatter in the regression…
Recent results have suggested that there is tension between the Gaia DR1 TGAS distances and the distances obtained using luminosities determined by eclipsing binaries or asteroseismology on red giant stars. We use the $K_s$-band…
In view of the great performance of circumcentered isometry methods for solving the best approximation problem, in this work we further investigate the locally proper circumcenter mapping and circumcentered method. Various examples of…