Related papers: Linear functions on the classical matrix groups

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…

Combining Stein's method with heat kernel techniques, we study the function Tr(AO), where A is a fixed n by n real matrix over such that Tr(AA^t)=n, and O is from the Haar measure of the orthogonal group O(n,R). It is shown that the total…

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…

We propose a new functional analytic approach to Stein's method of exchangeable pairs that does not require the pair at hand to satisfy any approximate linear regression property. We make use of this theory in order to derive abstract…

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…

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…

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…

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…

By the continuous mapping theorem, if a sequence of $d$-dimensional random vectors $(\mathbf{W}_n)_{n\geq1}$ converges in distribution to a multivariate normal random variable $\Sigma^{1/2}\mathbf{Z}$, then the sequence of random variables…

The topic of this paper is the asymptotic distribution of random orthogonal matrices distributed according to Haar measure. We examine the total variation distance between the joint distribution of the entries of $W_n$, the $p_n \times q_n$…

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 derive a new result for exponential approximation using Stein's method of exchangeable pairs. As an application, an exponential limit theorem with error term is derived for |Tr(U)|^2, where Tr(U) denotes the trace of a matrix chosen from…

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…

The purpose of this paper is to synthesize the approaches taken by Chatterjee-Meckes and Reinert-R\"ollin in adapting Stein's method of exchangeable pairs for multivariate normal approximation. The more general linear regression condition…

Motivated by the central limit problem for convex bodies, we study normal approximation of linear functionals of high-dimensional random vectors with various types of symmetries. In particular, we obtain results for distributions which are…

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…

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 work we study a version of the general question of how well a Haar distributed orthogonal matrix can be approximated by a random gaussian matrix. Here, we consider a gaussian random matrix $Y_n$ of order $n$ and apply to it the…

We show that the distance in total variation between $(\mathrm{Tr}\ U, \frac{1}{\sqrt{2}}\mathrm{Tr}\ U^2, \cdots, \frac{1}{\sqrt{m}}\mathrm{Tr}\ U^m)$ and a real Gaussian vector, where $U$ is a Haar distributed orthogonal or symplectic…

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…