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Related papers: Stein's method for the matrix normal distribution

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The generalized hyperbolic (GH) distributions form a five parameter family of probability distributions that includes many standard distributions as special or limiting cases, such as the generalized inverse Gaussian distribution, Student's…

Probability · Mathematics 2017-12-15 Robert E. Gaunt

Starting from the probability distribution of finite N-body systems, which maximises the Havrda--Charv\'at entropy, we build a Stein-type goodness-of-fit test. The Maxwell--Boltzmann distribution is exact only in the thermodynamic limit,…

Mathematical Physics · Physics 2026-02-16 Jae Wan Shim

Edgeworth expansion provides higher-order corrections to the normal approximation for a probability distribution. The classical proof of Edgeworth expansion is via characteristic functions. As a powerful method for distributional…

Probability · Mathematics 2022-11-09 Xiao Fang , Song-Hao Liu

In this paper, we quantify some known approximation to the Curie-Weiss model via applying the Stein method to the Markov chain whose stationary distribution coincides with Curie-Weiss model.

Probability · Mathematics 2021-02-22 Yingdong Lu

In this paper we propose tight upper and lower bounds for the Wasserstein distance between any two {{univariate continuous distributions}} with probability densities $p_1$ and $p_2$ having nested supports. These explicit bounds are…

Probability · Mathematics 2015-10-21 Christophe Ley , Gesine Reinert , Yvik Swan

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

We develop a new technique, based on Stein's method, for comparing two stationary distributions of irreducible Markov Chains whose update rules are `close enough'. We apply this technique to compare Ising models on $d$-regular expander…

Probability · Mathematics 2018-09-18 Guy Bresler , Dheeraj M. Nagaraj

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…

Probability · Mathematics 2010-05-18 Sourav Chatterjee , Elizabeth Meckes

We develop Stein's method for the Fr\'echet distribution and apply it to compute rates of convergence in distribution of renormalized sample maxima to the Fr\'echet distribution.

Probability · Mathematics 2013-11-18 Carine Bartholmé , Yvik Swan

The Wasserstein distance between probability measures on compact spaces provides a natural invariant quantitative measure of equidistribution, which is partly similar to the classical discrepancy appearing in Erd\"os-Tur\'an type…

Number Theory · Mathematics 2025-07-29 Emmanuel Kowalski , Théo Untrau

Distributional comparison is a fundamental problem in statistical data analysis with numerous applications in a variety of scientific and engineering fields. Numerous methods exist for distributional comparison but kernel Stein's method has…

Statistics Theory · Mathematics 2025-06-12 Xiaoda Qu , Baba C. Vemuri

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…

Probability · Mathematics 2014-07-07 Xiao Fang

Wasserstein distributionally robust optimization offers a framework for model fitting in machine learning under potential shifts in the data distribution. We study a regularized variant of this problem in which entropic smoothing produces a…

Optimization and Control · Mathematics 2026-05-28 Tam Le

Applying an inductive technique for Stein and zero bias couplings yields Berry-Esseen theorems for normal approximation for two new examples. The conditions of the main results do not require that the couplings be bounded. Our two…

Probability · Mathematics 2020-05-12 Louis H. Y. Chen , Larry Goldstein , Adrian Röllin

In a recent paper by the authors, a new approach--called the "embedding method"--was introduced, which allows to make use of exchangeable pairs for normal and multivariate normal approximation with Stein's method in cases where the…

Probability · Mathematics 2009-12-18 Gesine Reinert , Adrian Röllin

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

The notion of entropy-regularized optimal transport, also known as Sinkhorn divergence, has recently gained popularity in machine learning and statistics, as it makes feasible the use of smoothed optimal transportation distances for data…

Statistics Theory · Mathematics 2019-11-05 Jérémie Bigot , Elsa Cazelles , Nicolas Papadakis

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 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…

Probability · Mathematics 2009-04-03 Nathan Ross

We combine Stein's method with Malliavin calculus in order to obtain explicit bounds in the multidimensional normal approximation (in the Wasserstein distance) of functionals of Gaussian fields. Our results generalize and refine the main…

Probability · Mathematics 2008-11-19 Ivan Nourdin , Giovanni Peccati , Anthony Réveillac