Related papers: Concentration inequalities for randomly permuted s…
New nonuniform Berry--Esseen-type bounds for sums of independent random variables are obtained, motivated by recent studies concerning such bounds for nonlinear statistics. The proofs are based on the Chen--Shao concentration techniques…
Consider two random variables contaminated by two unknown transformations. The aim of this paper is to test the equality of those transformations. Two cases are distinguished: first, the two random variables have known distributions.…
We give concentration bounds for martingales that are uniform over finite times and extend classical Hoeffding and Bernstein inequalities. We also demonstrate our concentration bounds to be optimal with a matching anti-concentration…
Concentration inequalities are fundamental tools in probabilistic combinatorics and theoretical computer science for proving that random functions are near their means. Of particular importance is the case where f(X) is a function of…
Matrix concentration inequalities, intimately connected to the Non-Commutative Khintchine inequality, have been an important tool in both applied and pure mathematics. We study tensor versions of these inequalities, and establish…
A general method for obtaining moment inequalities for functions of independent random variables is presented. It is a generalization of the entropy method which has been used to derive concentration inequalities for such functions…
We prove several new results on the Hamming weight of bounded uniform and small-bias distributions. We exhibit bounded-uniform distributions whose weight is anti-concentrated, matching existing concentration inequalities. This construction…
We derive transport-entropy inequalities for mixed binomial point processes, and for Poisson point processes. We show that when the finite intensity measure satisfies a Talagrand transport inequality, the law of the point process also…
We establish both uniform and nonuniform error bounds of the Berry-Esseen type in normal approximation under local dependence. These results are of an order close to the best possible if not best possible. They are more general or sharper…
We introduce a version of Stein's method for proving concentration and moment inequalities in problems with dependence. Simple illustrative examples from combinatorics, physics, and mathematical statistics are provided.
We show that, under mild assumptions, the spectrum of a sum of independent random matrices is close to that of the Gaussian random matrix whose entries have the same mean and covariance. This nonasymptotic universality principle yields…
We prove concentration inequalities for several models of non-linear random matrices. As corollaries we obtain estimates for linear spectral statistics of the conjugate kernel of neural networks and non-commutative polynomials in (possibly…
In this short note we derive concentration inequalities for the empirical absolute moments of square symmetric matrices with independent symmetrically distributed +/-1 entries. Most of the previous results of this type are limited to…
Considering supercritical Bernoulli percolation on $\mathbb{Z}^d$, Garet and Marchand [GM09] proved a diffusive concentration for the graph distance. In this paper, we sharpen this result by establishing the subdiffusive concentration…
In this paper we give optimal constants in Talagrand's concentration inequalities for maxima of empirical processes associated to independent and eventually nonidentically distributed random variables. Our approach is based on the entropy…
Permutation tests date back nearly a century to Fisher's randomized experiments, and remain an immensely popular statistical tool, used for testing hypotheses of independence between variables and other common inferential questions. Much of…
We present nonasymptotic concentration inequalities for sums of independent and identically distributed random variables that yield asymptotic strong Gaussian approximations of Koml\'os, Major, and Tusn\'ady (KMT) [1975,1976]. The constants…
We prove a multivariate version of Bernstein's inequality about the probability that degenerate $U$-statistics take a value larger than some number $u$. This is an improvement of former estimates for the same problem which yields an…
We derive simple concentration inequalities for bounded random vectors, which generalize Hoeffding's inequalities for bounded scalar random variables. As applications, we apply the general results to multinomial and Dirichlet distributions…
For general repeated measures designs the Wald-type statistic (WTS) is an asymptotically valid procedure allowing for unequal covariance matrices and possibly non-normal multivariate observations. The drawback of this procedure is the poor…