相关论文: Stein's method, Palm theory and Poisson process ap…

This paper concerns the development of Stein's method for chi-square approximation and its application to problems in statistics. New bounds for the derivatives of the solution of the gamma Stein equation are obtained. These bounds involve…

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…

We introduce the observable Wasserstein distance, a framework for deriving lower bounds on the Wasserstein distance between probability measures on Polish metric spaces, designed to bypass the computational intractability of exact optimal…

We consider the Gaussian approximation for functionals of a Poisson process that are expressible as sums of region-stabilizing (determined by the points of the process within some specified regions) score functions and provide a bound on…

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…

We extend Stein's lemma for averages that explicitly contain the Gaussian random variable at a power. We present two proofs for this extension of Stein's lemma, with the first being a rigorous proof by mathematical induction. The…

Stein's method (Stein, 1973; 1981) is a powerful tool for statistical applications and has significantly impacted machine learning. Stein's lemma plays an essential role in Stein's method. Previous applications of Stein's lemma either…

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…

Let $\xi$ be the stationary occupation field generated by a Poisson system of independent simple symmetric random walks on $\mathbb Z$ in space--time dimension $1+1$. For a finite set $A\subset\mathbb Z$, we consider the classical…

We introduce a new version of Stein's method that reduces a large class of normal approximation problems to variance bounding exercises, thus making a connection between central limit theorems and concentration of measure. Unlike Skorokhod…

By exploiting the well-known observation that size-biasing or zero-biasing an infinitely divisible random variable may be achieved by adding an independent increment, combined with tools from Stein's method for compound Poisson and Gaussian…

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…

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…

This article develops, and describes how to use, results concerning disintegrations of Poisson random measures. These results are fashioned as simple tools that can be tailor-made to address inferential questions arising in a wide range of…

In this article, we provide an extension of the Chen-Stein inequality for Poisson approximation in the total variation distance for sums of independent Bernoulli random variables in two ways. We prove that we can improve the rate of…

We build on the formalism developed in [arXiv:1906.08372v1] to propose new representations of solutions to Stein equations. We provide new uniform and non uniform bounds on these solutions (a.k.a.\ Stein factors). We use these…

Stein's method is a powerful technique for proving central limit theorems in probability theory when more straightforward approaches cannot be implemented easily. This article begins with a survey of the historical development of Stein's…

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…

Statistical models often include thousands of parameters. However, large models decrease the investigator's ability to interpret and communicate the estimated parameters. Reducing the dimensionality of the parameter space in the estimation…

The concentration inequality approach for normal approximation by Stein's method is generalized to the multivariate setting. We use this approach to prove a non-smooth function distance for multivariate normal approximation for standardized…