相关论文: An explicit Berry-Ess\'een bound for uniformly exp…
The asymptotic constant in the Berry-Esseen inequality for interval probabilities is shown to be sqrt(2/pi).
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…
Expanding maps with indifferent fixed points, a.k.a. intermittent maps, are popular models in nonlinear dynamics and infinite ergodic theory. We present a simple proof of the exactness of a wide class of expanding maps of [0,1], with…
A new Berry-Esseen bound for non-linear functionals of non-symmetric and non-homogeneous infinite Rademacher sequences is established. It is based on a discrete version of the Malliavin-Stein method and an analysis of the discrete…
For complex multiple Wiener-It\^{o} integral, we present Berry-Ess\'een upper and lower bounds in terms of moments and kernel contractions under the Wasserstein distance. As a corollary, we simplify the previously known contraction…
Let $\mu$ be a probability measure on $\text{GL}_d(\mathbb{R})$ and denote by $S_n:= g_n \cdots g_1$ the associated random matrix product, where $g_j$ are i.i.d. with law $\mu$. Under the assumptions that $\mu$ has a finite exponential…
It is shown that the absolute constant in the Berry--Esseen inequality for i.i.d. Bernoulli random variables is strictly less than the Esseen constant, if $1\le n\le 500000$, where $n$ is a number of summands. This result is got both with…
In this article, we obtain explicit bounds on the uniform distance between the cumulative distribution function of a standardized sum $S_n$ of $n$ independent centered random variables with moments of order four and its first-order…
A nonuniform version of the Berry-Esseen bound has been proved. The most important feature of the new bound is a monotonically decreasing function C(|t|) instead of the universal constant C=29.1174: C(|t|)<C if |t| > 3.2, and C(|t|) tends…
In this paper, we prove a Berry--Esseen bound with optimal order for self-normalized sums of local dependent random variables under some mild dependence conditions. The proof is based on Stein's method and a randomized concentration…
Let $(g_{n})_{n\geq 1}$ be a sequence of independent and identically distributed positive random $d\times d$ matrices and consider the matrix product $G_n: = g_n \ldots g_1$. Under suitable conditions, we establish the Berry-Esseen bounds…
This paper establishes a non-uniform Berry--Esseen bound for non-normal approximation using Stein's method. The main theorem generalizes the result of the authors in [Comptes Rendus Mathematique, 2024] to the context of non-normal…
This manuscript studies the Gaussian approximation of the coordinate-wise maximum of self-normalized statistics in high-dimensional settings. We derive an explicit Berry-Esseen bound under weak assumptions on the absolute moments. When the…
In this paper, the uniformly asymptotic normality for sample quantiles of associated random variables is investigated under some conditions on the decay of the covariances. We obtain the rate of normal approximation of order…
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…
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…
Berry-Esseen-type bounds for total variation and relative entropy distances to the normal law are established for the sums of non-i.i.d. random variables.
Non-asymptotic bounds for Gaussian and bootstrap approximation have recently attracted significant interest in high-dimensional statistics. This paper studies Berry-Esseen bounds for such approximations with respect to the multivariate…
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…
Two different aspects of parabolic iteration in the complex upper half-plane are considered here. First, from a noncommutative probability perspective, a Berry-Esseen type estimate for the convergence speed of the monotone central limit…