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Related papers: Variance-Gamma approximation via Stein's method

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In this paper, we consider a target random variable $Y \sim \CVG$ distributed according to a centered Variance--Gamma distribution. For a generic random element $F=I_2(f)$ in the second Wiener chaos with $\E[F^2]= \E[Y^2]$ we establish a…

Probability · Mathematics 2021-07-01 Ehsan Azmoodeh , Peter Eichelsbacher , Christoph Thäle

Let $\{X_{i}, i\in J\}$ be a family of locally dependent non-negative integer-valued random variables with finite expectations and variances. We consider the sum $W=\sum_{i\in J}X_i$ and use Stein's method to establish general upper error…

Probability · Mathematics 2024-11-26 Zhonggen Su , Xiaolin Wang

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

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…

Statistics Theory · Mathematics 2026-01-19 Robert E. Gaunt , Frédéric Ouimet , Donald Richards

In this article, we present the theoretical basis for an approach to Stein's method for probability distributions on Riemannian manifolds. Using a semigroup representation for the solution to the Stein equation, we use tools from stochastic…

Probability · Mathematics 2020-01-28 James Thompson

We study the Stein equation associated with the one-dimensional Gamma distribution, and provide novel bounds, allowing one to effectively deal with test functions supported by the whole real line. We apply our estimates to derive new…

Probability · Mathematics 2017-03-14 Christian Döbler , Giovanni Peccati

In this paper, we obtain error bound for binomial and negative binomial approximations to weighted sums of locally dependent random variables, using Stein's method. We also discuss approximation results for weighted sums of independent…

Probability · Mathematics 2020-10-20 Amit N. Kumar

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…

Probability · Mathematics 2025-10-28 Paul Mansanarez , Guillaume Poly , Yvik Swan

In this paper, we consider the sums of non-negative integer valued $m$-dependent random variables, and its approximation to the power series distribution. We first discuss some relevant results for power series distribution such as Stein…

Probability · Mathematics 2020-05-05 Amit N. Kumar , Neelesh S. Upadhye , P. Vellaisamy

We provide a general steady-state diffusion approximation result which bounds the Wasserstein distance between the reversible measure $\mu$ of a diffusion process and the measure $\nu$ of an approximating Markov chain. Our result is…

Probability · Mathematics 2022-03-15 Thomas Bonis

In this article, we derive Stein's method for approximating a spatial random graph by a generalised random geometric graph, which has vertices given by a finite Gibbs point process and edges based on a general connection function. Our main…

Probability · Mathematics 2024-11-06 Dominic Schuhmacher , Leoni Carla Wirth

We use Stein's method to obtain a bound on the distance between scaled $p$-dimensional random walks and a $p$-dimensional (correlated) Brownian Motion. We consider dependence schemes including those in which the summands in scaled sums are…

Probability · Mathematics 2020-06-09 Mikołaj J. Kasprzak

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 present a de Bruijn type approximation for quantifying the content of m smooth numbers, derived from samples obtained through a probability measure over the set of integers less than or equal to n, with point mass function at k inversely…

Probability · Mathematics 2025-03-04 Arturo Jaramillo , Xiaochuan Yang

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 present a straightforward formulation of Stein's method for the semicircular distribution, specifically designed for the analysis of non-commutative random variables. Our approach employs a non-commutative version of Stein's heuristic,…

Probability · Mathematics 2024-12-03 Mario Díaz , Arturo Jaramillo

We develop a new formulation of Stein's method to obtain computable upper bounds on the total variation distance between the geometric distribution and a distribution of interest. Our framework reduces the problem to the construction of a…

Probability · Mathematics 2013-03-21 Erol A. Peköz , Adrian Röllin , Nathan Ross

This paper is concerned with the Stein's method associated with a (possibly) asymmetric $\alpha$-stable distribution $Z$, in dimension one. More precisely, its goal is twofold. In the first part, we exhibit a genuine bound for the…

Probability · Mathematics 2018-09-12 Peng Chen , Ivan Nourdin , Lihu Xu

We build upon recent advances on the distributional aspect of Stein's method to propose a novel and flexible technique for computing Stein operators for random variables that can be written as products of independent random variables. We…

Probability · Mathematics 2018-09-28 Robert E. Gaunt , Guillaume Mijoule , Yvik Swan

Let $W$ be a random variable with mean zero and variance $\sigma^2$. The distribution of a variate $W^*$, satisfying $EWf(W)=\sigma ^2 Ef'(W^*)$ for smooth functions $f$, exists uniquely and defines the zero bias transformation on the…

Probability · Mathematics 2007-05-23 Larry Goldstein , Gesine Reinert