Related papers: Non-uniform Berry-Esseen theorems for weakly depen…
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…
A gem of classical probability, the Berry-Esseen theorem provides a non-asymptotic form of the central limit theorem. This note gives a friendly and intuitive exposition of the classical Fourier-analytic proof of Esseen's smoothing…
We provide a Lyapunov type bound in the multivariate central limit theorem for sums of independent, but not necessarily identically distributed random vectors. The error in the normal approximation is estimated for certain classes of sets,…
Certain smoothing inequalities were proposed in the recent paper posted on arXiv at arxiv:1301.2828 in order to lessen the very large gap between the best correctly established upper and lower bounds on the constant factor in the nonuniform…
Given a weakly dependent stationary process, we describe the transition between a Berry-Esseen bound and a second order Edgeworth expansion in terms of the Berry-Esseen characteristic. This characteristic is sharp: We show that Edgeworth…
In this paper we give new deviation inequalities of Bernstein's type for the partial sums of weakly dependent time series. The loss from the independent case is studied carefully. We give non mixing examples such that dynamical systems and…
We consider statistical learning question for $\psi$-weakly dependent processes, that unifies a large class of weak dependence conditions such as mixing, association,$\cdots$ The consistency of the empirical risk minimization algorithm 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 $X_1,\ldots,X_N$ be i.i.d.\ random variables distributed like $X$. Suppose that the first $k \geq 3$ moments $\{ \mathbb{E}[X^j] : j = 1,\ldots,k\}$ of $X$ agree with that of the standard Gaussian distribution, that…
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…
Moment inequalities play important roles in probability limit theory and mathematical statistics. In this work, the von Bahr-Esseen type inequality for extended negatively dependent random variables under sub-linear expectations is…
We establish a new Bernstein-type deviation inequality for general (non-reversible) discrete-time Markov chains via an elementary approach. More robust than existing works in the literature, our result only requires the Markov chain to…
We study the random conductance model on the lattice $\mathbb{Z}^d$, i.e. we consider a linear, finite-difference, divergence-form operator with random coefficients and the associated random walk under random conductances. We allow the…
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,…
We propose classification schemes for characterizing two-dimensional topological phases with nontrivial weak indices. Here, "weak" implies that the Chern number in the corresponding phase is trivial, while the system shows edge states along…
We consider the stochastic integrals of multivariate point processes and study their concentration phenomena. In particular, we obtain a Bernstein type of concentration inequality through Dol\'eans-Dade exponential formula and a uniform…
In this paper we survey some recent results on the central limit theorem and its weak invariance principle for stationary sequences. We also describe several maximal inequalities that are the main tool for obtaining the invariance…
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…
In this paper we obtain non-uniform Berry-Esseen bounds for normal approximations by the Malliavin-Stein method. The techniques rely on a detailed analysis of the solutions of Stein's equations and will be applied to functionals of a…
This paper deals with the quantitative normal approximation of non-linear functionals of Poisson random measures, where the quality is measured by the Kolmogorov distance. Combining Stein's method with the Malliavin calculus of variations…