相关论文: Stein's method and the rank distribution of random…

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…

Stein's method compares probability distributions through the study of a class of linear operators called Stein operators. While mainly studied in probability and used to underpin theoretical statistics, Stein's method has led to…

Let $\{X_{i}, i\in J\}$ be a family of locally dependent non-negative integer-valued random variables with finite expectations and variances. We consider the sum $W=\sum_{i\in J}X_i$ and use Stein's method to establish general upper error…

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…

One of the major themes of random matrix theory is that many asymptotic properties of traditionally studied distributions of random matrices are universal. We probe the edges of universality by studying the spectral properties of random…

We obtain rates of convergence in limit theorems of partial sums $S_n$ for certain sequences of dependent, identically distributed random variables, which arise naturally in statistical mechanics, in particular, in the context of the…

Let $W$ be a random variable with mean zero and variance $\sigma^2$. The distribution of a variate $W^*$, satisfying $EWf(W)=\sigma ^2 Ef'(W^*)$ for smooth functions $f$, exists uniquely and defines the zero bias transformation on the…

We generalize the well-known zero bias distribution and the $\lambda$-Stein pair to an approximate zero bias distribution and an approximate $\lambda,R$-Stein pair, respectively. Berry Esseen type bounds to the normal, based on approximate…

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 propose a modification to the density approach to Stein's method for intervals for the unit circle $\mathbb{S}^1$ which is motivated by the differing geometry of $\mathbb{S}^1$ to Euclidean space. We provide an upper bound…

Let $\mathbf{a}_{ij}$, $1\leq i\leq j\leq n$, be independent random variables and $\mathbf{a}_{ji}=\mathbf{a}_{ij}$, for all $i,j$. Suppose that every $\mathbf{a}_{ij}$ is bounded, has zero mean, and its variance is given by…

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…

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…

Consider a uniformly chosen random reduced decomposition of the longest element in the symmetric group. It is known that the location of the first transposition in this decomposition converges to the semicircle distribution. In this note we…

We establish inequalities for assessing the distance between the distribution of errors of partially observed high-frequency statistics of multidimensional L\'evy processes and that of a mixed Gaussian random variable. Furthermore, we…

We consider a general preferential attachment model, where the probability that a newly arriving vertex connects to an older vertex is proportional to a sublinear function of the indegree of the older vertex at that time. It is well known…

The random matrix uniformly distributed over the set of all m-by-n matrices over a finite field plays an important role in many branches of information theory. In this paper a generalization of this random matrix, called k-good random…

We develop a variant of Stein's method of comparison of generators to bound the Kolmogorov, total variation, and Wasserstein-1 distances between distributions on the real line. Our discrepancy is expressed in terms of the ratio of reverse…

We extend our previous study of Markov chains on finite commutative rings (arXiv:1605.05089) to arbitrary finite rings with identity. At each step, we either add or multiply by a randomly chosen element of the ring, where the addition…

We discuss Stein's method for approximation by the stationary distribution of a single-birth Markov chain, in conjunction with stochastic monotonicity and similar assumptions. We use bounds on the increments of the solution of Poisson's…