Related papers: Strong Gaussian Approximation for the Sum of Rando…

Optimal transport has emerged as a fundamental methodology with applications spanning multiple research areas in recent years. However, the convergence rate of the empirical estimator to its population counterpart suffers from the curse of…

This study develops a non-asymptotic Gaussian approximation theory for distributions of M-estimators, which are defined as maximizers of empirical criterion functions. In existing mathematical statistics literature, numerous studies have…

We consider the classification problem of a high-dimensional mixture of two Gaussians with general covariance matrices. Using the replica method from statistical physics, we investigate the asymptotic behavior of a general class of…

We propose flexible Gaussian representations for conditional cumulative distribution functions and give a concave likelihood criterion for their estimation. Optimal representations satisfy the monotonicity property of conditional cumulative…

In this paper an analytic expression is given for the bounds of the distribution function of the sum of dependent normally distributed random variables. Using the theory of copulas and the important Frechet bounds the dependence structure…

We establish Gaussian limits for general measures induced by binomial and Poisson point processes in d-dimensional space. The limiting Gaussian field has a covariance functional which depends on the density of the point process. The general…

We obtain new bounds for the optimal matching cost for empirical measures with unbounded support. For a large class of radially symmetric and rapidly decaying probability laws, we prove for the first time the asymptotic rate of convergence…

We consider a finite sequence of random points in a finite domain of a finite-dimensional Euclidean space. The points are sequentially allocated in the domain according to a model of cooperative sequential adsorption. The main peculiarity…

This article derives quantitative limit theorems for multivariate Poisson and Poisson process approximations. Employing the solution of Stein's equation for Poisson random variables, we obtain an explicit bound for the multivariate Poisson…

Motivated by modern data forms such as images and multi-view data, the multi-attribute graphical model aims to explore the conditional independence structure among vectors. Under the Gaussian assumption, the conditional independence between…

Using proof-theoretic methods in the style of proof mining, we give novel computationally effective limit theorems for the convergence of the Cesaro-means of certain sequences of random variables. These results are intimately related to…

Improving Importance Sampling estimators for rare event probabilities requires sharp approx- imations of the optimal density leading to a nearly zero-variance estimator. This paper presents a new way to handle the estimation of the…

Examples with bound information on the regression function and density abound in many real applications. We propose a novel approach for estimating such functions by incorporating the prior knowledge on the bounds. Specially, a Gaussian…

In this paper, we obtain error bound for binomial and negative binomial approximations to weighted sums of locally dependent random variables, using Stein's method. We also discuss approximation results for weighted sums of independent…

We consider the famous Rasch model, which is applied to psychometric surveys when n persons under test answer m questions. The score is given by a realization of a random binary (n,m)-matrix. Its (j,k)th component indicates whether or not…

We investigate the link between regularised self-transport problems and maximum likelihood estimation in Gaussian mixture models (GMM). This link suggests that self-transport followed by a clustering technique leads to principled estimators…

In this work, we investigate an optimization problem over adapted couplings between pairs of real valued random variables, possibly describing random times. We relate those couplings to a specific class of causal transport plans between…

We obtain a tight distribution-specific characterization of the sample complexity of large-margin classification with L2 regularization: We introduce the margin-adapted dimension, which is a simple function of the second order statistics of…

We study the discrepancy between the distribution of a vector-valued functional of i.i.d. random elements and that of a Gaussian vector. Our main contribution is an explicit bound on the convex distance between the two distributions,…

Measuring dependence between random variables is a fundamental problem in Statistics, with applications across diverse fields. While classical measures such as Pearson's correlation have been widely used for over a century, they have…