Related papers: On Stein's method for multivariate normal approxim…
Let $M$ be a random matrix in the orthogonal group $\O_n$, distributed according to Haar measure, and let $A$ be a fixed $n\times n$ matrix over $\R$ such that $\tr(AA^t)=n$. Then the total variation distance of the random variable…
We propose a new general version of Stein's method for univariate distributions. In particular we propose a canonical definition of the Stein operator of a probability distribution {which is based on a linear difference or differential-type…
We prove a general theorem to bound the total variation distance between the distribution of an integer valued random variable of interest and an appropriate discretized normal distribution. We apply the theorem to 2-runs in a sequence of…
We extend Stein's celebrated Wasserstein bound for normal approximation via exchangeable pairs to the multi-dimensional setting. As an intermediate step, we exploit the symmetry of exchangeable pairs to obtain an error bound for smooth test…
In this paper we develop a framework for multivariate functional approximation by a suitable Gaussian process via an exchangeable pairs coupling that satisfies a suitable approximate linear regression property, thereby building on work by…
Variance-Gamma distributions are widely used in financial modelling and contain as special cases the normal, Gamma and Laplace distributions. In this paper we extend Stein's method to this class of distributions. In particular, we obtain a…
We develop Stein's method for the half-normal distribution and apply it to derive rates of convergence in distributional limit theorems for three statistics of the simple symmetric random walk: the maximum value, the number of returns to…
We provide a new general theorem for multivariate normal approximation on convex sets. The theorem is formulated in terms of a multivariate extension of Stein couplings. We apply the results to a homogeneity test in dense random graphs and…
Motivated by its appearance as a limiting distribution for random and non-random sums of independent random variables, in this paper we develop Stein's method for approximation by the asymmetric Laplace distribution. Our results generalise…
It is shown that the method of exchangeable pairs introduced by Stein [Approximate Computation of Expectations (1986) IMS, Hayward, CA] for normal approximation can effectively be used for translated Poisson approximation. Introducing an…
We use Stein's method to obtain explicit bounds on the rate of convergence for the Laplace approximation of two different sums of independent random variables; one being a random sum of mean zero random variables and the other being a…
Motivated by the omnipresence of extreme value distributions in limit theorems involving extremes of random processes, we adapt Stein's method to include these laws as possible target distributions. We do so by using the generator approach…
This paper provides a general framework for Stein's density method for multivariate continuous distributions. The approach associates to any probability density function a canonical operator and Stein class, as well as an infinite…
We show by a surprisingly simple argument that the exchangeability condition, which is key to the exchangeable pair approach in Stein's method for distributional approximation, can be omitted in many standard settings. This is achieved by…
Narayana numbers appear in many places in combinatorics and probability, and it is known that they are asymptotically normal. Using Stein's method of exchangeable pairs, we provide an error of approximation in total variation to a symmetric…
This paper is concerned with the Stein's method associated with a (possibly) asymmetric $\alpha$-stable distribution $Z$, in dimension one. More precisely, its goal is twofold. In the first part, we exhibit a genuine bound for the…
We present a straightforward formulation of Stein's method for the semicircular distribution, specifically designed for the analysis of non-commutative random variables. Our approach employs a non-commutative version of Stein's heuristic,…
In Stein's method, the exchangeable pair approach is commonly used to estimate the approximation errors in normal approximation. In this paper, we establish a Cram\'er-type moderate deviation theorem of normal approximation for unbounded…
This paper is a short exposition of Stein's method of normal approximation from my personal perspective. It focuses mainly on the characterization of the normal distribution and the construction of Stein identities. Through examples, it…
In this paper we extend Stein's method to the distribution of the product of $n$ independent mean zero normal random variables. A Stein equation is obtained for this class of distributions, which reduces to the classical normal Stein…