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This paper deals with bilateral-gamma (BG) approximation to functionals of an isonormal Gaussian process. We use Malliavin-Stein method to obtain the error bounds for the smooth Wasserstein distance. As by-products, the error bounds for…

Probability · Mathematics 2024-10-01 Kalyan Barman , Tomoyuki Ichiba , Palaniappan Vellaisamy

In this paper, we extend Stein's method to products of independent beta, gamma, generalised gamma and mean zero normal random variables. In particular, we obtain Stein operators for mixed products of these distributions, which include the…

Probability · Mathematics 2018-04-18 Robert E. Gaunt

In this paper, a new method based on probability generating functions is used to obtain multiple Stein operators for various random variables closely related to Poisson, binomial and negative binomial distributions. Also, Stein operators…

Probability · Mathematics 2016-05-10 N. S. Upadhye , V. Cekanavicius , P. Vellaisamy

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 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

This paper deals with Poisson approximation to weighted sums of locally dependent random variables using Stein's method. The derived result represents a significant improvement of existing results. To illustrate the effectiveness of our…

Probability · Mathematics 2023-12-08 Pratima Eknath Kadu

We generalize the well-known zero bias distribution and the $\lambda$-Stein pair to an approximate zero bias distribution and an approximate $\lambda,R$-Stein pair, respectively. Berry Esseen type bounds to the normal, based on approximate…

Probability · Mathematics 2017-11-27 Nathakhun Wiroonsri

We develop Stein's method for the half-normal distribution and apply it to derive rates of convergence in distributional limit theorems for three statistics of the simple symmetric random walk: the maximum value, the number of returns to…

Probability · Mathematics 2015-11-24 Christian Döbler

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 propose a new version of Stein's method of exchangeable pairs, which, given a suitable exchangeable pair $(W,W')$ of real-valued random variables, suggests the approximation of the law of $W$ by a suitable absolutely continuous…

Probability · Mathematics 2015-10-21 Christian Döbler

Over the last 80 years there has been much interest in the problem of finding an explicit formula for the probability density function of two zero mean correlated normal random variables. Motivated by this historical interest, we use a…

Statistics Theory · Mathematics 2021-04-13 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

We obtain almost optimal convergence rate in the central limit theorem for "nonconevntional" sums of the form $S_N=N^{-\frac12}\sum_{n=1}^N (F(\xi_n,\xi_{2n},...,\xi_{\ell n})-\bar F)$.

Probability · Mathematics 2018-01-08 Yeor Hafouta

Stein's method is used to study discrete representations of multidimensional distributions that arise as approximations of states of quantum harmonic oscillators. These representations model how quantum effects result from the interaction…

Probability · Mathematics 2021-05-31 Ian W. McKeague , Yvik Swan

We explore negative dependence and stochastic orderings, showing that if an integer-valued random variable $W$ satisfies a certain negative dependence assumption, then $W$ is smaller (in the convex sense) than a Poisson variable of equal…

Probability · Mathematics 2016-01-22 Fraser Daly

In this paper, we obtain Stein operator for sum of $n$ independent random variables (rvs) which is shown as perturbation of negative binomial (NB) operator. Comparing the operator with NB operator, we derive the error bounds for total…

Probability · Mathematics 2020-07-16 A. N. Kumar , N. S. Upadhye

A stochastic ordering approach is applied with Stein's method for approximation by the equilibrium distribution of a birth-death process. The usual stochastic order and the more general s-convex orders are discussed. Attention is focused on…

Probability · Mathematics 2009-12-09 Fraser Daly , Claude Lefèvre , Sergey Utev

We develop a multidimensional Stein methodology for non-degenerate self-decomposable random vectors in $\mathbb{R}^d$ having finite first moment. Building on previous univariate findings, we solve an integro-partial differential Stein…

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

We combine Malliavin calculus with Stein's method to derive bounds for the Variance-Gamma approximation of functionals of isonormal Gaussian processes, in particular of random variables living inside a fixed Wiener chaos induced by such a…

Probability · Mathematics 2014-09-22 Peter Eichelsbacher , Christoph Thäle

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