相关论文: Rates of convergence towards the Fr\'echet distrib…

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 provide optimal rates of convergence to the asymptotic distribution of the (properly scaled) degree of a fixed vertex in two preferential attachment random graph models. Our approach is to show that these distributions are unique fixed…

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…

The block maxima method in extreme-value analysis proceeds by fitting an extreme-value distribution to a sample of block maxima extracted from an observed stretch of a time series. The method is usually validated under two simplifying…

We use Stein's method to obtain bounds on the rate of convergence for a class of statistics in geometric probability obtained as a sum of contributions from Poisson points which are exponentially stabilizing, i.e. locally determined in a…

Using Stein's method techniques, we develop a framework which allows one to bound the error terms arising from approximation by the Laplace distribution and apply it to the study of random sums of mean zero random variables. As a corollary,…

In this paper, we propose a new distribution with unitary support which can be characterized as a ratio of the type $W=X_1/(X_1+X_2)$, where $(X_1, X_2)^\top$ follows a bivariate extreme distribution with Fr\'echet margins, that is, $X_1$…

We give the rate of convergence of some optimal lower Riemann-Stieltjes sums toward the integral.

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…

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…

This paper introduces a new approach to the study of rates of convergence for posterior distributions. It is a natural extension of a recent approach to the study of Bayesian consistency. In particular, we improve on current rates of…

For a skew normal random sequence, convergence rates of the distribution of its partial maximum to the Gumbel extreme value distribution are derived. The asymptotic expansion of the distribution of the normalized maximum is given under an…

Gradient information on the sampling distribution can be used to reduce the variance of Monte Carlo estimators via Stein's method. An important application is that of estimating an expectation of a test function along the sample path of a…

As an application of Stein's method for Poisson approximation, we prove rates of convergence for the tail probabilities of two scan statistics that have been suggested for detecting local signals in sequences of independent random variables…

Given a distribution $\rho$ on persistence diagrams and observations $X_1,...X_n \stackrel{iid}{\sim} \rho$ we introduce an algorithm in this paper that estimates a Fr\'echet mean from the set of diagrams $X_1,...X_n$. If the underlying…

Stein's method is used to approximate sums of discrete and locally dependent random variables by a centered and symmetric Binomial distribution. Under appropriate smoothness properties of the summands, the same order of accuracy as in the…

Using Stein's method for the Beta distributions and a recent technique by Goldstein and Reinert of comparing the Stein characterization of the target distribution with that of the approximating distribution we prove a rate of convergence in…

The main result of the article is the rate of convergence to the Rosenblatt-type distributions in non-central limit theorems. Specifications of the main theorem are discussed for several scenarios. In particular, special attention is paid…

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 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…