Related papers: Refined Berry-Esseen bounds under local dependence

We provide a general result for bounding the difference between point probabilities of integer supported distributions and the translated Poisson distribution, a convenient alternative to the discretized normal. We illustrate our theorem in…

Testing network effects in weighted directed networks is a foundational problem in econometrics, sociology, and psychology. Yet, the prevalent edge dependency poses a significant methodological challenge. Most existing methods are…

Stein's method is used to approximate sums of discrete and locally dependent random variables by a centered and symmetric Binomial distribution. Under appropriate smoothness properties of the summands, the same order of accuracy as in the…

We obtain explicit Berry-Esseen bounds in the Kolmogorov distance for the normal approximation of non-linear functionals of vectors of independent random variables. Our results are based on the use of Stein's method and of random difference…

Uniform and nonuniform Berry--Esseen (BE) bounds of optimal orders on the closeness to normality for general abstract nonlinear statistics are given, which are then used to obtain optimal bounds on the rate of convergence in the delta…

We prove a Berry-Esseen theorem, a local central limit theorem and (local) large and (global) moderate deviations principles for i.i.d. (uniformly) random non-uniformly expanding or hyperbolic maps with exponential first return times. Using…

We adapt Stein's method to obtain Berry--Esseen type error bounds in the multivariate central limit theorem for non-stationary processes generated by time-dependent compositions of uniformly expanding dynamical systems. In a particular case…

In this note, we provide a Berry--Esseen bounds for rectangles in high-dimensions when the random vectors have non-singular covariance matrices. Under this assumption of non-singularity, we prove an $n^{-1/2}$ scaling for the Berry--Esseen…

For uniformly expanding maps on the interval, analogous versions of the Berry-Ess\'een theorem are known but only with an unexplicit upper bound in $O(1/\sqrt{n})$ without any constants being specified. In this paper, we use the recent…

We prove semi-empirical concentration inequalities for random variables which are given as possibly nonlinear functions of independent random variables. These inequalities describe concentration of random variable in terms of the…

Consider the set of all sequences of $n$ outcomes, each taking one of $m$ values, that satisfy a number of linear constraints. If $m$ is fixed while $n$ increases, most sequences that satisfy the constraints result in frequency vectors…

We consider the problem of bounding large deviations for non-i.i.d. random variables that are allowed to have arbitrary dependencies. Previous works typically assumed a specific dependence structure, namely the existence of independent…

We derive explicit central moment inequalities for random variables that admit a Stein coupling, such as exchangeable pairs, size--bias couplings or local dependence, among others. The bounds are in terms of moments (not necessarily…

Consider a stationary, weakly dependent sequence of random variables. Given only mild conditions, allowing for polynomial decay of the autocovariance function, we show a Berry-Esseen bound of optimal order $n^{-1/2}$ for studentized…

In the present paper, we derive Berry-Esseen bounds for the estimation of diversity indices on countable alphabets. A general non-asymptotic convergence rate is established for the plug-in estimator of a wide class of indices, including…

In this paper, we study the self-normalized Cram\a'{e}r-type moderate deviations for centered independent random variables $X_1, X_2,...$ with $0<E |X_i|^3 <\infty$. The main results refine Theorems 1.1 and 1.2 of Wang (2011), the…

General Berry-Esseen bounds are developed for the exponential distribution using Stein's method. As an application, a sharp error term is obtained for Hora's result that the spectrum of the Bernoulli-Laplace Markov chain has an exponential…

Due to the effort of a number of authors, the value c_u of the absolute constant factor in the uniform Berry--Esseen (BE) bound for sums of independent random variables has been gradually reduced to 0.4748 in the iid case and 0.5600 in the…

We introduce a new family of distributions to approximate $\mathbb {P}(W\in A)$ for $A\subset\{...,-2,-1,0,1,2,...\}$ and $W$ a sum of independent integer-valued random variables $\xi_1$, $\xi_2$, $...,$ $\xi_n$ with finite second moments,…

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.