Related papers: Exponential approximation and Stein's method of ex…
Stein's method of exchangeable pairs is examined through five examples in relation to Poisson and normal distribution approximation. In particular, in the case where the exchangeable pair is constructed from a reversible Markov chain, we…
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…
An exchangeable pair approach is commonly taken in the normal and non-normal approximation using Stein's method. It has been successfully used to identify the limiting distribution and provide an error of approximation. However, when the…
We combine the method of exchangeable pairs with Stein's method for functional approximation. As a result, we give a general linearity condition under which an abstract Gaussian approximation theorem for stochastic processes holds. We apply…
Let W be either the number of descents or inversions of a permutation. Stein's method is applied to show that W satisfies a central limit theorem with error rate n^(-1/2). The construction of an exchangeable pair (W,W') used in Stein's…
Since the introduction of Stein's method in the early 1970s, much research has been done in extending and strengthening it; however, there does not exist a version of Stein's original method of exchangeable pairs for multivariate normal…
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…
In this paper we establish a multivariate exchangeable pairs approach within the framework of Stein's method to assess distributional distances to potentially singular multivariate normal distributions. By extending the statistics into a…
We construct a continuous family of exchangeable pairs by perturbing the random variable through diffusion processes on manifold in order to apply Stein method to certain geometric settings. We compare our perturbation by diffusion method…
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…
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 show how the infinitesimal exchangeable pairs approach to Stein's method combines naturally with the theory of Markov semigroups. We present a multivariate normal approximation theorem for functions of a random variable invariant with…
The purpose of this dissertation is to introduce a version of Stein's method of exchangeable pairs to solve problems in measure concentration. We specifically target systems of dependent random variables, since that is where the power of…
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…
It is known that the fluctuations of suitable linear statistics of Haar distributed elements of the compact classical groups satisfy a central limit theorem. We show that if the corresponding test functions are sufficiently smooth, a rate…
Stein's method is used to prove limit theorems for random character ratios. Tools are developed for four types of structures: finite groups, Gelfand pairs, twisted Gelfand pairs, and association schemes. As one example an error term is…
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…
In a recent paper by the authors, a new approach--called the "embedding method"--was introduced, which allows to make use of exchangeable pairs for normal and multivariate normal approximation with Stein's method in cases where the…
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…
In the seventies, Charles Stein revolutionized the way of proving the Central Limit Theorem by introducing a method that utilizes a characterization equation for Gaussian distribution. In the last 50 years, much research has been done to…