Related papers: Berry-Esseen bounds for functionals of independent…
A judicious application of the Berry-Esseen theorem via suitable Augustin information measures is demonstrated to be sufficient for deriving the sphere packing bound with a prefactor that is…
We prove concentration inequalities for functions of independent random variables {under} sub-gaussian and sub-exponential conditions. The utility of the inequalities is demonstrated by an extension of the now classical method of Rademacher…
This paper establishes a non-uniform Berry--Esseen bound in normal approximation for exchangeable pairs using Stein's method via a concentration inequality approach. The main theorem extends and improves several results in the literature,…
A sum of observations derived by a simple random sampling design from a population of independent random variables is studied. A procedure finding a general term of Edgeworth asymptotic expansion is presented. The Lindeberg condition of…
We investigate the asymptotic behavior of eigenfunctions of the Laplacian on Riemannian manifolds. We show that Benjamini-Schramm convergence provides a unified language for the level and eigenvalue aspects of the theory. As a result, we…
In this work we study the rate of convergence in the central limit theorem for the Euclidean norm of random orthogonal projections of vectors chosen at random from an $\ell_p^n$-ball which has been obtained in [Alonso-Guti\'errez, Prochno,…
We derive Cram\'{e}r type moderate deviations for stationary sequences of bounded random variables. Our results imply the moderate deviation principles and a Berry-Esseen bound. Applications to quantile coupling inequalities, functions of…
We derive a Gaussian Central Limit Theorem for the sample quantiles based on locally dependent random variables with explicit convergence rate. Our approach is based on converting the problem to a sum of indicator random variables, applying…
The aim of this paper is to present a new proof of an explicit version of the Berry-Ess\'{e}en type inequality of Bolthausen (Zeitschrift f\"ur Wahrscheinlichkeitstheorie und Verwandte Gebiete, 66, 379--386, 1984). The literature already…
We analyze a natural extension of the backward Euler approximation for a class of BSDEs with Lipschitz generators and random (unbounded) time horizons. We derive strong error bounds in terms of the underlying stepsize; the distance between…
We show sharp bounds for probabilities of large deviations for sums of independent random variables satisfying Bernstein's condition. One such bound is very close to the tail of the standard Gaussian law in certain case; other bounds…
A sharp, distribution free, non-asymptotic result is proved for the concentration of a random function around the mean function, when the randomization is generated by a finite sequence of independent data and the random functions satisfy…
We study higher order expansions both in the Berry-Ess\'een estimate (Edgeworth expansions) and in the local limit theorems for Birkhoff sums of chaotic probability preserving dynamical systems. We establish general results under technical…
The paper establishes a functional version of the Hoeffding combinatorial central limit theorem. First, a pre-limiting Gaussian process approximation is defined, and is shown to be at a distance of the order of the Lyapounov ratio from the…
We consider two-dimensional determinantal processes which are rotation-invariant and study the fluctuations of the number of points in disks. Based on the theory of mod-phi convergence, we obtain Berry-Esseen as well as precise moderate to…
For an Ornstein-Uhlenbeck process driven by a fractional Brownian motion with Hurst parameter 0<H<1/2, one shows the Berry-Ess\'een bound of the least squares estimator of the drift parameter. Thus, a problem left in the previous paper…
We study function estimation in the empirical Bayes setting for Poisson and normal means. Specifically, given observations $Y_i\sim f(\cdot; \theta_i)$ with latent parameters $\theta_i\sim \pi$, the goal is to estimate…
In this paper, we are concerned with multivariate Gegenbauer approximation of functions defined in the $d$-dimensional hypercube. Two new and sharper bounds for the coefficients of multivariate Gegenbauer expansion of analytic functions are…
In this paper, we establish non-uniform Berry-Esseen bounds by means of the Malliavin-Stein method. Applications to the multiple Wiener-It\^o integrals and the exponential functionals of Brownian motion are given to illustrate the theory.
This paper proves a Berry--Esseen theorem for sample quantiles of strongly-mixing random variables under a polynomial mixing rate. The rate of normal approximation is shown to be $O(n^{-1/2})$ as $n\to\infty$, where $n$ denotes the sample…