Related papers: A conditional Berry-Esseen inequality

In this paper, a new technique is introduced to obtain non-uniform Berry-Esseen bounds of normal and nonnormal approximation for unbounded exchangeable pairs. This technique does not rely on the concentration inequalities developed by Chen…

We prove a Berry-Esseen theorem and Edgeworth expansions for partial sums of the form $S_N=\sum_{n=1}^{N}f_n(X_n,X_{n+1})$, where $\{X_n\}$ is a uniformly elliptic inhomogeneous Markov chain and $\{f_n\}$ is a sequence of uniformly bounded…

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 study the self-normalized sums of independent random variables from the perspective of the Malliavin calculus. We give the chaotic expansion for them and we prove a Berry-Ess\'een bound with respect to several distances.

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,…

Berry-Esseen-type bounds are developed in the multidimensional local limit theorem in terms of the Lyapunov coefficients and maxima of involved densities.

We consider the random walk among random conductances on Z^d. We assume that the conductances are independent, identically distributed and uniformly bounded away from 0 and infinity. We obtain a quantitative version of the central limit…

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 give a nonuniform Berry-Esseen bound for self-normalized martingales, which bridges the gap between the result of Haeusler (1988) and Fan and Shao (2018). The bound coincides with the nonuniform Berry-Esseen bound of Haeusler and Joos…

Let $H$ be a real separable Hilbert space and $(a_k)_{k\in\mathbb{Z}}$ a sequence of bounded linear operators from $H$ to $H$. We consider the linear process $X$ defined for any $k$ in $\mathbb{Z}$ by…

We provide bounds of Berry-Esseen type for fundamental limit theorems in operator-valued free probability theory such as the operator-valued free Central Limit Theorem and the asymptotic behaviour of distributions of operator-valued…

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…

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…

A powerful robust mean estimator introduced by Catoni (2012) allows for mean estimation of heavy-tailed data while achieving the performance characteristics of classical mean estimator for sub-Gaussian data. While Catoni's framework has…

The inductive size bias coupling technique and Stein's method yield a Berry-Esseen theorem for the number of urns having occupancy $d \ge 2$ when $n$ balls are uniformly distributed over $m$ urns. In particular, there exists a constant $C$…

Hwang's quasi-power theorem asserts that a sequence of random variables whose moment generating functions are approximately given by powers of some analytic function is asymptotically normally distributed. This theorem is generalised to…

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…

We address the question of a Berry Esseen type theorem for the speed of convergence in a multivariate free central limit theorem. For this, we estimate the difference between the operator-valued Cauchy transforms of the normalized partial…

In this work the $\ell_q$-norms of points chosen uniformly at random in a centered regular simplex in high dimensions are studied. Berry-Esseen bounds in the regime $1\leq q < \infty$ are derived and complemented by a non-central limit…

A distributional symmetry is invariance of a distribution under a group of transformations. Exchangeability and stationarity are examples. We explain that a result of ergodic theory provides a law of large numbers: If the group satisfies…