Related papers: Stein's method and the Laplace distribution
We establish a general Berry-Esseen type bound which gives optimal bounds in many situations under suitable moment assumptions. By combining the general bound with Palm theory, we deduce a new error bound for assessing the accuracy of…
In this article, we develop Stein characterization for two-sided tempered stable distribution. Stein characterizations for normal, gamma, Laplace, and variance-gamma distributions already known in the literature follow easily. One can also…
We use the Stein-Chen method to prove new explicit inequalities for the total variation, Wasserstein and local distances between the distribution of a random diagonal sum of a Bernoulli matrix and a Poisson distribution. Approximation…
This survey article discusses the main concepts and techniques of Stein's method for distributional approximation by the normal, Poisson, exponential, and geometric distributions, and also its relation to concentration inequalities. The…
Stein's method allows to prove distributional convergence of a sequence of random variables and to quantify it with respect to a given metric such as Kolmogorov's (a Berry-Ess\'een type theorem). Mod-* convergence quantifies the convergence…
Over the last 80 years there has been much interest in the problem of finding an explicit formula for the probability density function of two zero mean correlated normal random variables. Motivated by this historical interest, we use a…
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…
This work presents the first systematic development of Stein's method for matrix distributions. We establish the basic essential ingredients of Stein's method for matrix normal approximation: we derive a generator-based Stein identity from…
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,…
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,…
In the context of bounding probability of small deviation, there are limited general tools. However, such bounds have been widely applied in graph theory and inventory management. We introduce a common approach to substantially sharpen such…
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…
In this article, we present the theoretical basis for an approach to Stein's method for probability distributions on Riemannian manifolds. Using a semigroup representation for the solution to the Stein equation, we use tools from stochastic…
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…
\noindent We study the asymptotic behavior of a sum of independent and identically distributed random variables conditioned by a sum of independent and identically distributed integer-valued random variables. We prove a Berry-Esseen bound…
In this paper, we establish Berry--Esseen bounds for both self-normalized and non-self-normalized sums of locally dependent random variables. The proofs are based on Stein's method together with a concentration inequality approach. We…
We take another look at using Stein's method to establish uniform Berry-Esseen bounds for Studentized nonlinear statistics, highlighting variable censoring and an exponential randomized concentration inequality for a sum of censored…
Let $\boldsymbol{\xi}=(\xi_1,\ldots,\xi_m)$ be a negatively associated mean zero random vector with components that obey the bound $|\xi_i| \le B, i=1,\ldots,m$, and whose sum $W = \sum_{i=1}^m \xi_i$ has variance 1, the bound \[…
Motivated by a theorem of Barbour, we revisit some of the classical limit theorems in probability from the viewpoint of the Stein method. We setup the framework to bound Wasserstein distances between some distributions on infinite…
Stein's method provides a way of bounding the distance of a probability distribution to a target distribution $\mu$. Here we develop Stein's method for the class of discrete Gibbs measures with a density $e^V$, where $V$ is the energy…