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Related papers: Stein's method for concentration inequalities

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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,…

Probability · Mathematics 2014-10-29 John Pike , Haining Ren

We use Stein characterizations to obtain new moment-type estimators for the parameters of three classical spherical distributions (namely the Fisher-Bingham, the von Mises-Fisher, and the Watson distributions) in the i.i.d. case. This leads…

Statistics Theory · Mathematics 2024-07-05 Adrian Fischer , Robert E. Gaunt , Yvik Swan

We present, in a unified way, a Stein methodology for infinitely divisible laws (without Gaussian component) having finite first moment. Based on a correlation representation, we obtain a characterizing non-local Stein operator which boils…

Probability · Mathematics 2019-04-08 Benjamin Arras , Christian Houdré

Stein's method is applied to obtain a general Cramer-type moderate deviation result for dependent random variables whose dependence is defined in terms of a Stein identity. A corollary for zero-bias coupling is deduced. The result is also…

Probability · Mathematics 2013-02-06 Louis H. Y. Chen , Xiao Fang , Qi-Man Shao

Initially motivated by the study of the non-asymptotic properties of non-parametric tests based on permutation methods, concentration inequalities for uniformly permuted sums have been largely studied in the literature. Recently, Delyon et…

Probability · Mathematics 2018-05-10 Mélisande Albert

We study an approximation method of stationary characters of a two-dimensional Markov chain via the Stein method. For this purpose, innovative methods are developed to estimate the moments of the Markov chain, as well as the solution to the…

Probability · Mathematics 2021-12-13 Yingdong Lu

The "variance method" has been used to prove many classical inequalities in design theory and coding theory. The purpose of this expository note is to review and present some of these inequalities in a unified setting. I will also discuss…

Combinatorics · Mathematics 2025-05-30 Douglas R. Stinson

A Stein-Tomas type inequality and a (weak) decoupling inequality are proved by using the polynomial partitioning method. Both estimates are related closely to Waring's problem.

Classical Analysis and ODEs · Mathematics 2023-09-25 Xiaochun Li

Simple inequalities are established for some integrals involving the modified Bessel functions of the first and second kind. In most cases, we show that we obtain the best possible constant or that our bounds are tight in certain limits. We…

Classical Analysis and ODEs · Mathematics 2018-02-09 Robert E. Gaunt

We extend Stein's method to include independence with respect to an auxiliary random variable, for any law for which a Stein characterization does exist. This extends the current literature on the problem. Using tools from the Malliavin…

Probability · Mathematics 2026-05-04 Aleksandar Balašev-Samarski , Abdol-Reza Mansouri

This work explores and develops elements of Stein's method of approximation, in the infinitely divisible setting, and its connections to functional analysis. It is mainly concerned with multivariate self-decomposable laws without finite…

Probability · Mathematics 2019-11-12 Benjamin Arras , Christian Houdré

For any discrete target distribution, we exploit the connection between Markov chains and Stein's method via the generator approach and express the solution of Stein's equation in terms of expected hitting time. This yields new upper bounds…

Probability · Mathematics 2018-02-16 Michael C. H. Choi

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 introduce a version of Stein's method of comparison of operators specifically tailored to the problem of bounding the Wasserstein-1 distance between continuous and discrete distributions on the real line. Our approach rests on a new…

Probability · Mathematics 2023-11-03 Gilles Germain , Yvik Swan

This work obtains sharp closed-form exponential concentration inequalities of Bernstein type for the ubiquitous beta distribution, improving upon sub-gaussian and sub-gamma bounds previously studied in this context. The proof leverages a…

Probability · Mathematics 2024-10-21 Maciej Skorski

We show that a special case of method of moment estimator derived from the Stein class coincides with the class of generalized score matching estimator. Choosing a suitable weight function for generalized score matching is not…

Methodology · Statistics 2026-02-09 Alfred Kume , Stephen G. Walker

Let $S_{n}$ be a sum of independent identically distribution random variables with finite first moment and $h_{M}$ be a call function defined by $g_{M}(x)=\max\{x-M,0\}$ for $x\in\mathbb{R}$, $M>0$. In this paper, we assume the random…

Probability · Mathematics 2024-11-26 Peng Chen , Tianyi Qi , Ting Zhang

Via a covariance representation based on characteristic functions, a known elementary proof of the Gaussian concentration inequality is presented. A few other applications are briefly mentioned.

Probability · Mathematics 2024-10-10 Christian Houdré

We use a generalization of Hoeffding's inequality to show concentration results for the free energy of disordered pinning models, assuming only that the disorder has a finite exponential moment. We also prove some concentration inequalities…

Probability · Mathematics 2012-06-15 Frederique Watbled

This note provides the Stein equation for weighted sums of independent $\chi^{2}$ distributions.

Probability · Mathematics 2020-02-25 Xiaohui Chen , Partha Dey