Related papers: Approximation of Riemannian measures by Stein's me…
We obtain bounds to quantify the distributional approximation in the delta method for vector statistics (the sample mean of $n$ independent random vectors) for normal and non-normal limits, measured using smooth test functions. For normal…
The Wasserstein distance quantifies the distance between two probability measures on a metric space. We prove an analogue of the Berry-Esseen inequality for the Wasserstein distance on a finite area hyperbolic surface. This inequality…
In (Barbour, 1990) foundations for diffusion approximation via Stein's method are laid. This paper has been cited more than 130 times and is a cornerstone in the area of Stein's method. A semigroup argument is used therein to solve a Stein…
We develop Stein's method for $\alpha$-stable approximation with $\alpha\in(0,1]$, continuing the recent line of research by Xu \cite{lihu} and Chen, Nourdin and Xu \cite{C-N-X} in the case $\alpha\in(1,2).$ The main results include an…
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…
The squared Wasserstein distance is a natural quantity to compare probability distributions in a non-parametric setting. This quantity is usually estimated with the plug-in estimator, defined via a discrete optimal transport problem which…
In this paper, we study statistical inference for the Wasserstein distance, which has attracted much attention and has been applied to various machine learning tasks. Several studies have been proposed in the literature, but almost all of…
The Steiner ratio characterizes the greatest possible deviation of the length of a minimal spanning tree from the length of the minimal Steiner tree. In this paper, estimates of the Steiner ratio on Riemannian manifolds are obtained. As a…
We establish a general inequality on the Poisson space, yielding an upper bound for the distance in total variation between the law of a regular random variable with values in the integers and a Poisson distribution. Several applications…
We derive normal approximation bounds in the Wasserstein distance for sums of weighted U-statistics, based on a general distance bound for functionals of independent random variables of arbitrary distributions. Those bounds are applied to…
In this paper, we consider the problem of propagating an uncertain distribution by a possibly non-linear function and quantifying the resulting uncertainty. We measure the uncertainty using the Wasserstein distance, and for a given input…
We derive Stein approximation bounds for functionals of uniform random variables, using chaos expansions and the Clark-Ocone representation formula combined with derivation and finite difference operators. This approach covers sums and…
This paper considers the entropy of the sum of (possibly dependent and non-identically distributed) Bernoulli random variables. Upper bounds on the error that follows from an approximation of this entropy by the entropy of a Poisson random…
We obtain Stein approximation bounds for stochastic integrals with respect to a Poisson random measure over ${\Bbb R}^d$, $d\geq 2$. This approach relies on third cumulant Edgeworth-type expansions based on derivation operators defined by…
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…
Estimating means on Riemannian manifolds is generally computationally expensive because the Riemannian distance function is not known in closed-form for most manifolds. To overcome this, we show that Riemannian diffusion means can be…
We address the problem of efficiently computing Wasserstein distances for multiple pairs of distributions drawn from a meta-distribution. To this end, we propose a fast estimation method based on regressing Wasserstein distance on sliced…
Assume that we observe i.i.d.~points lying close to some unknown $d$-dimensional $\mathcal{C}^k$ submanifold $M$ in a possibly high-dimensional space. We study the problem of reconstructing the probability distribution generating the…
We develop a general framework for statistical inference with the 1-Wasserstein distance. Recently, the Wasserstein distance has attracted considerable attention and has been widely applied to various machine learning tasks because of its…
In this article, we obtain, for the total variance distance, the error bounds between Poisson and convolution of power series distributions via Stein's method. This provides a unified approach to many known discrete distributions. Several…