Related papers: A conditional Berry-Esseen inequality
We prove Berry-Esseen type rates of convergence for central limit theorems (CLTs) of regenerative processes which generalize previous results of Bolthausen under weaker moment assumptions. We then show how this general result can be applied…
We obtain a sharp estimate of the speed of convergence in the Boolean central limit theorem for measures of finite sixth moment. The main tool is a quantitative version of the Stieltjes-Perron inversion formula.
In this article we present a Bernstein inequality for sums of random variables which are defined on a spatial lattice structure. The inequality can be used to derive concentration inequalities. It can be useful to obtain consistency…
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…
Suppose that the (normalised) partial sum of a stationary sequence converges to a standard normal random variable. Given sufficiently moments, when do we have a rate of convergence of $n^{-1/2}$ in the uniform metric, in other words, when…
Let $(Z_n)$ be a supercritical branching process in a random environment $\xi = (\xi_n)$. We establish a Berry-Esseen bound and a Cram\'er's type large deviation expansion for $\log Z_n$ under the annealed law $\mathbb P$. We also improve…
Under correlation-type conditions, we derive upper bounds of order $\frac{1}{\sqrt{n}}$ for the Kolmogorov distance between the distributions of weighted sums of dependent summands and the normal law.
In this paper, we propose a new approach for deriving probabilistic inequalities. Our main idea is to exploit the information of underlying distributions by virtue of the monotone likelihood ratio property and Berry-Essen inequality.…
The asymptotic constant in the Berry-Esseen inequality for interval probabilities is shown to be sqrt(2/pi).
We give rates of convergence in the Central Limit Theorem for the coefficients and the spectral radius of the left random walk on GLd(R), assuming the existence of an exponential or polynomial moment.
An optimal bound on the quantiles of a certain kind of distributions is given. Such a bound is used in applications to Berry--Esseen-type bounds for nonlinear statistics.
A central limit theorem for arrays of symmetric row-wise exchangeable random variables is presented. The result is valid for finite and infinite extendable and non-extendable sequences. Unlike most reported versions of the central limit…
Let $X_n=\sum_{i=1}^{\infty}a_i\epsilon_{n-i}$, where the $\epsilon_i$ are i.i.d. with mean 0 and at least finite second moment, and the $a_i$ are assumed to satisfy $|a_i|=O(i^{-\beta})$ with $\beta >1/2$. When $1/2<\beta<1$, $X_n$ is…
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…
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…
We study accuracy of bootstrap procedures for estimation of quantiles of a smooth function of a sum of independent sub-Gaussian random vectors. We establish higher-order approximation bounds with error terms depending on a sample size and a…
In this paper, we give the central limit theorem and almost sure central limit theorem for products of some partial sums of independent identically distributed random variables.
A central limit theorem is established for a sum of random variables belonging to a sequence of random fields. The fields are assumed to have zero mean conditional on the past history and to satisfy certain conditional $\alpha$-mixing…
Let $\{Z_n, n\geq 0\}$ be a supercritical branching process in an independent and identically distributed random environment. We prove Cram\'{e}r moderate deviations and Berry-Esseen bounds for $\ln (Z_{n+n_0}/Z_{n_0})$ % under the annealed…
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…