Related papers: K-minus Estimator Approach to Large Scale Structur…
In this paper, we present a unified analysis of both convergence and optimality of adaptive mixed finite element methods for a class of problems when the finite element spaces and corresponding a posteriori error estimates under…
We develop and analyse residual-based a posteriori error estimates for the virtual element discretisation of a nonlinear stress-assisted diffusion problem in two and three dimensions. The model problem involves a two-way coupling between…
We consider the problem of estimating a $d$-dimensional $s$-sparse discrete distribution from its samples observed under a $b$-bit communication constraint. The best-known previous result on $\ell_2$ estimation error for this problem is…
Statistical testing is widespread and critical for a variety of scientific disciplines. The advent of machine learning and the increase of computing power has increased the interest in the analysis and statistical testing of…
For any finite point set in $D$-dimensional space equipped with the 1-norm, we present random linear embeddings to $k$-dimensional space, with a new metric, having the following properties. For any pair of points from the point set that are…
The level curvature distribution function is studied both analytically and numerically for the case of T-breaking perturbations over the orthogonal ensemble. The leading correction to the shape of the curvature distribution beyond the…
This work proposes $\chi^2$-type test statistics to assess different hypotheses on the local structure of an observed marked point pattern. The test statistics is based on the local inhomogeneous extension of the mark-weighted $K$-function…
The current methods available to estimate gravitational shear from astronomical images of galaxies introduce systematic errors which can affect the accuracy of weak lensing cosmological constraints. We study the impact of KSB shape…
We present a localized a-posteriori error estimate for the localized reduced basis multi-scale (LRBMS) method [Albrecht, Haasdonk, Kaulmann, Ohlberger (2012): The localized reduced basis multiscale method]. The LRBMS is a combination of…
We revisit the problem of estimating the mean of a real-valued distribution, presenting a novel estimator with sub-Gaussian convergence: intuitively, "our estimator, on any distribution, is as accurate as the sample mean is for the Gaussian…
We study the accuracy of estimating the covariance and the precision matrix of a $D$-variate sub-Gaussian distribution along a prescribed subspace or direction using the finite sample covariance. Our results show that the estimation…
Measuring the two-point correlation function of the galaxies in the Universe gives access to the underlying dark matter distribution, which is related to cosmological parameters and to the physics of the primordial Universe. The estimation…
We study the properties of the set of marginal distributions of infinite translation-invariant systems in the 2D square lattice. In cases where the local variables can only take a small number $d$ of possible values, we completely solve the…
We study the scaling scenery of Gibbs measures for subshifts of finite type on self-conformal fractals and applications to Falconer's distance set problem and dimensions of projections. Our analysis includes hyperbolic Julia sets, limit…
We consider the popular $k$-means problem in $d$-dimensional Euclidean space. Recently Friggstad, Rezapour, Salavatipour [FOCS'16] and Cohen-Addad, Klein, Mathieu [FOCS'16] showed that the standard local search algorithm yields a…
We consider the eigenvalue problem $K x = \lambda x$. Our analysis focuses on the convergence rates of eigenvalue and spectral subspace approximations for compact linear integral operator $K$ with Green's kernels. By employing orthogonal…
The aim of this paper is to introduce new statistical criterions for estimation, suitable for inference in models with common continuous support. This proposal is in the direct line of a renewed interest for divergence based inference tools…
We show that for families of measures on Euclidean space which satisfy an ergodic-theoretic form of "self-similarity" under the operation of re-scaling, the dimension of linear images of the measure behaves in a semi-continuous way. We…
Accepting validity of self-consistent theory of localization by Vollhardt and Woelfle, we derive the finite-size scaling procedure used for studies of the critical behavior in d-dimensional case and based on the use of auxiliary quasi-1D…
Public health data are often spatially dependent, but standard spatial regression methods can suffer from bias and invalid inference when the independent variable is associated with spatially-correlated residuals. This could occur if, for…