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Related papers: Stein's method for max-stable random vectors

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Stein's method is used to obtain two theorems on multivariate normal approximation. Our main theorem, Theorem 1.2, provides a bound on the distance to normality for any nonnegative random vector. Theorem 1.2 requires multivariate size bias…

Probability · Mathematics 2007-05-23 Larry Goldstein , Yosef Rinott

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…

Probability · Mathematics 2017-05-30 Robert E. Gaunt

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…

Probability · Mathematics 2007-05-23 Mathew D. Penrose , J. E. Yukich

We use Stein's method to establish the rates of normal approximation in terms of the total variation distance for a large class of sums of score functions of marked Poisson point processes on $\mathbb{R}^d$. As in the study under the weaker…

Probability · Mathematics 2020-11-17 Tianshu Cong , Aihua Xia

In this article, we first obtain, for the Kolmogorov distance, an error bound between a tempered stable and a compound Poisson distribution and also an error bound between a tempered stable and an alpha stable distribution via Stein method.…

Probability · Mathematics 2024-08-20 Kalyan Burman , Neelesh S Upadhye , Palaniappan Vellaisamy

Stein's method provides a way of bounding the distance of a probability distribution to a target distribution $\mu$. Here we develop Stein's method for the class of discrete Gibbs measures with a density $e^V$, where $V$ is the energy…

Probability · Mathematics 2008-08-22 Peter Eichelsbacher , Gesine Reinert

We consider $M/Ph/n+M$ queueing systems in steady state. We prove that the Wasserstein distance between the stationary distribution of the normalized system size process and that of a piecewise Ornstein-Uhlenbeck (OU) process is bounded by…

Probability · Mathematics 2015-12-01 Anton Braverman , J. G. Dai

In this paper, we use Stein's method to obtain optimal bounds, both in Kolmogorov and in Wasserstein distance, in the normal approximation for the empirical distribution of the ground state of a many-interacting-worlds harmonic oscillator…

Probability · Mathematics 2022-03-30 Louis H. Y. Chen , Lê Vǎn Thành

The Stein's method is a popular method used to derive upper-bounds of distances between probability distributions. It can be viewed, in certain of its formulations, as an avatar of the semi-group or of the smart-path method used commonly in…

Probability · Mathematics 2015-05-25 Laurent Decreusefond

The Wasserstein distance is a distance between two probability distributions and has recently gained increasing popularity in statistics and machine learning, owing to its attractive properties. One important approach to extending this…

Methodology · Statistics 2022-02-14 Ryo Okano , Masaaki Imaizumi

This paper provides an introduction to the Stein method framework in the context of steady-state diffusion approximations. The framework consists of three components: the Poisson equation and gradient bounds, generator coupling, and moment…

Probability · Mathematics 2017-02-21 Anton Braverman , J. G. Dai , Jiekun Feng

This work introduces a new, explicit bound on the Hellinger distance between a continuous random variable and a Gaussian with matching mean and variance. As example applications, we derive a quantitative Hellinger central limit theorem and…

Probability · Mathematics 2025-09-23 Morgane Austern , Lester Mackey

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…

Probability · Mathematics 2007-05-23 Adrian Röllin

We obtain upper bounds for the total variation distance between the distributions of two Gibbs point processes in a very general setting. Applications are provided to various well-known processes and settings from spatial statistics and…

Probability · Mathematics 2014-09-15 Dominic Schuhmacher , Kaspar Stucki

In the first part of the paper we use a new Fourier technique to obtain a Stein characterizations for random variables in the second Wiener chaos. We provide the connection between this result and similar conclusions that can be derived…

Probability · Mathematics 2016-01-14 Benjamin Arras , Ehsan Azmoodeh , Guillaume Poly , Yvik Swan

This paper provides a simple procedure to fit generative networks to target distributions, with the goal of a small Wasserstein distance (or other optimal transport costs). The approach is based on two principles: (a) if the source…

Machine Learning · Computer Science 2019-06-12 Yucheng Chen , Matus Telgarsky , Chao Zhang , Bolton Bailey , Daniel Hsu , Jian Peng

We introduce a distributionally robust maximum likelihood estimation model with a Wasserstein ambiguity set to infer the inverse covariance matrix of a $p$-dimensional Gaussian random vector from $n$ independent samples. The proposed model…

Optimization and Control · Mathematics 2018-05-21 Viet Anh Nguyen , Daniel Kuhn , Peyman Mohajerin Esfahani

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…

Probability · Mathematics 2017-05-30 Robert E. Gaunt , Alastair Pickett , Gesine Reinert

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…

Statistics Theory · Mathematics 2017-12-29 Chris J. Oates , Jon Cockayne , François-Xavier Briol , Mark Girolami

We consider distributional approximation by generalized Dickman distributions, which appear in number theory, perpetuities, logarithmic combinatorial structures and many other areas. We prove bounds in the Kolmogorov distance for the…

Probability · Mathematics 2022-11-21 Chinmoy Bhattacharjee , Matthias Schulte