Related papers: About the Stein equation for the generalized inver…

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…

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…

This paper provides a general framework for Stein's density method for multivariate continuous distributions. The approach associates to any probability density function a canonical operator and Stein class, as well as an infinite…

In this article, we develop Stein characterization for two-sided tempered stable distribution. Stein characterizations for normal, gamma, Laplace, and variance-gamma distributions already known in the literature follow easily. One can also…

In this study, a numerical quadrature for the generalized inverse Gaussian distribution is derived from the Gauss-Hermite quadrature by exploiting its relationship with the normal distribution. The proposed quadrature is not Gaussian, but…

We build on the formalism developed in [arXiv:1906.08372v1] to propose new representations of solutions to Stein equations. We provide new uniform and non uniform bounds on these solutions (a.k.a.\ Stein factors). We use these…

We provide a new perspective on Stein's so-called density approach by introducing a new operator and characterizing class which are valid for a much wider family of probability distributions on the real line. We prove an elementary…

Variance-Gamma distributions are widely used in financial modelling and contain as special cases the normal, Gamma and Laplace distributions. In this paper we extend Stein's method to this class of distributions. In particular, we obtain a…

We provide a general result for bounding the difference between point probabilities of integer supported distributions and the translated Poisson distribution, a convenient alternative to the discretized normal. We illustrate our theorem in…

The gamma difference distribution is defined as the difference of two gamma distributions, with in general different shape and rate parameters. Starting with knowledge of the corresponding characteristic function, a second order linear…

Several characterizations of the Generalized Inverse Gaussian (GIG) distribution have been proposed in the literature, especially over the past two decades. These characterization theorems are surveyed, and two new characterizations are…

In a recent paper, Gaunt 2020 extended Stein's method to limit distributions that can be represented as a function $g:\mathbb{R}^d\rightarrow\mathbb{R}$ of a centered multivariate normal random vector $\Sigma^{1/2}\mathbf{Z}$ with…

We propose a new general version of Stein's method for univariate distributions. In particular we propose a canonical definition of the Stein operator of a probability distribution {which is based on a linear difference or differential-type…

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…

For parameter estimation of continuous and discrete distributions, we propose a generalization of the method of moments (MM), where Stein identities are utilized for improved estimation performance. The construction of these Stein-type…

We extend Stein's lemma for averages that explicitly contain the Gaussian random variable at a power. We present two proofs for this extension of Stein's lemma, with the first being a rigorous proof by mathematical induction. The…

Stein operators are differential operators which arise within the so-called Stein's method for stochastic approximation. We propose a new mechanism for constructing such operators for arbitrary (continuous or discrete) parametric…

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…

In this paper, we address the problem of estimating a covariance matrix of a multivariate Gaussian distribution, relative to a Stein loss function, from a decision theoretic point of view. We investigate the case where the covariance matrix…

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…