Publications (53)
Integration by parts and representation of information functionals
Ivan Nourdin, Giovanni Peccati, Yvik Swan
We introduce a new formalism for computing expectations of functionals of arbitrary random vectors, by using generalised integration by parts formulae. In doing so we extend recent…
A note on one-dimensional Poincaré inequalities by Stein-type integration
Gilles Germain, Yvik Swan
We study the weighted Poincaré constant of a probability density with weight function using integration methods inspired by Stein's method. We obtain a new versio…
Stein's method and approximating the multidimensional quantum harmonic oscillator
Ian W. McKeague, Yvik Swan
Stein's method is used to study discrete representations of multidimensional distributions that arise as approximations of states of quantum harmonic oscillators. These representat…
Stein's method for comparison of univariate distributions
Christophe Ley, Gesine Reinert, Yvik Swan
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…
Stein operators, kernels and discrepancies for multivariate continuous distributions
Guillaume Mijoule, Gesine Reinert, Yvik Swan
In this paper we present a general framework for Stein's method for multivariate continuous distributions. The approach gives a collection of Stein characterisations, among which w…
One-Step R-Estimation in Linear Models with Stable Errors
Marc Hallin, Yvik Swan, Thomas Verdebout +1
Classical estimation techniques for linear models either are inconsistent, or perform rather poorly, under -stable error densities; most of them are not even rate-optimal. In t…
Parametric Stein operators and variance bounds
Christophe Ley, Yvik Swan
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…
Stein's Method of Moments
Bruno Ebner, Adrian Fischer, Robert E. Gaunt +2
Stein operators allow to characterise probability distributions via differential operators. Based on these characterisations, we develop a new method of point estimation for margin…
A stroll along the gamma
Benjamin Arras, Yvik Swan
We provide the first in-depth study of the "smart path" interpolation between an arbitrary probability measure and the gamma- distribution. We propose new explicit repres…
An algebra of Stein operators
Robert E. Gaunt, Guillaume Mijoule, Yvik Swan
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 b…
Split Conformal Prediction under Data Contamination
Jase Clarkson, Wenkai Xu, Mihai Cucuringu +2
Conformal prediction is a non-parametric technique for constructing prediction intervals or sets from arbitrary predictive models under the assumption that the data is exchangeable…
Rates of convergence towards the Fréchet distribution
Carine Bartholmé, Yvik Swan
We develop Stein's method for the Fréchet distribution and apply it to compute rates of convergence in distribution of renormalized sample maxima to the Fréchet distribution.
The Adaptive Sampling Revisited
Matthew Drescher, Guy Louchard, Yvik Swan
The problem of estimating the number of distinct keys of a large collection of data is well known in computer science. A classical algorithm is the adaptive sampling (AS).…
Efficient ANOVA for directional data
Christophe Ley, Yvik Swan, Thomas Verdebout
In this paper we tackle the ANOVA problem for directional data (with particular emphasis on geological data) by having recourse to the Le Cam methodology usually reserved for linea…
Stein's density approach and information inequalities
Christophe Ley, Yvik Swan
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 dis…
Optimal R-Estimation of a Spherical Location
Christophe Ley, Yvik Swan, Baba Thiam +1
In this paper, we provide -estimators of the location of a rotationally symmetric distribution on the unit sphere of . In order to do so we first prove the local asymptoti…
A bound on the 2-Wasserstein distance between linear combinations of independent random variables
Benjamin Arras, Ehsan Azmoodeh, Guillaume Poly +1
We provide a bound on a natural distance between finitely and infinitely supported elements of the unit sphere of , the space of real valued sequences with fi…
A new approach to the Stein-Tikhomirov method: with applications to the second Wiener chaos and Dickman convergence
Benjamin Arras, Guillaume Mijoule, Guillaume Poly +1
In this paper, we propose a general means of estimating the rate at which convergences in law occur. Our approach, which is an extension of the classical Stein-Tikhomirov method, r…
On the rate of convergence in de Finetti's representation theorem
Guillaume Mijoule, Giovanni Peccati, Yvik Swan
A consequence of de Finetti's representation theorem is that for every infinite sequence of exchangeable 0-1 random variables , there exists a probability measure $…
One-dimensional Stein's method with bespoke derivatives
Gilles Germain, Yvik Swan
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 dist…
Derivatives of entropy and the MMSE conjecture
Paul Mansanarez, Guillaume Poly, Yvik Swan
We investigate the entropy of a probability measure along the heat flow and more precisely we seek for closed algebraic representations of its derivatives. Provided…
Edgeworth expansion on Wiener chaos
Paul Mansanarez, Guillaume Poly, Yvik Swan
Consider an element of the -th Wiener chaos $\WW_p$, and denote by $\prob_F$ its law. For a positive integer , let be the Radon measure with density…
Stein's method on the second Wiener chaos : 2-Wasserstein distance
Benjamin Arras, Ehsan Azmoodeh, Guillaume Poly +1
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…
Entropy and the fourth moment phenomenon
Ivan Nourdin, Giovanni Peccati, Yvik Swan
We develop a new method for bounding the relative entropy of a random vector in terms of its Stein factors. Our approach is based on a novel representation for the score function o…
On a connection between Stein characterizations and Fisher information
Christophe Ley, Yvik Swan
We generalize the so-called density approach to Stein characterizations of probability distributions. We prove an elementary factorization property of the resulting Stein operator…
Some new Stein operators for product distributions
Robert E. Gaunt, Guillaume Mijoule, Yvik Swan
We provide a general result for finding Stein operators for the product of two independent random variables whose Stein operators satisfy a certain assumption, extending a recent r…
On Hodges and Lehmann's " result"
Marc Hallin, Thomas Verdebout, Yvik Swan
While the asymptotic relative efficiency (ARE) of Wilcoxon rank-based tests for location and regression with respect to their parametric Student competitors can be arbitrarily larg…
Discrete Stein characterizations and discrete information distances
Christophe Ley, Yvik Swan
We construct two different Stein characterizations of discrete distributions and use these to provide a natural connection between Stein characterizations for discrete distribution…
A note on the normal approximation error for randomly weighted self-normalized sums
Siegfried Hoermann, Yvik Swan
Let $\bX=\{X_n\}_{n\geq 1}$ and $\bY=\{Y_n\}_{n\geq 1}$ be two independent random sequences. We obtain rates of convergence to the normal law of randomly weighted self-normalized s…
Stein characterizations for linear combinations of gamma random variables
Benjamin Arras, Ehsan Azmoodeh, Guillaume Poly +1
In this paper we propose a new, simple and explicit mechanism allowing to derive Stein operators for random variables whose characteristic function satisfies a simple ODE. We apply…
Local Pinsker inequalities via Stein's discrete density approach
Christophe Ley, Yvik Swan
Pinsker's inequality states that the relative entropy between two random variables and dominates the square of the total variation distance $d_{\mat…
Distances between nested densities and a measure of the impact of the prior in Bayesian statistics
Christophe Ley, Gesine Reinert, Yvik Swan
In this paper we propose tight upper and lower bounds for the Wasserstein distance between any two {univariate continuous distributions} with probability densities and …
Stein's method of moments for truncated multivariate distributions
Adrian Fischer, Robert E. Gaunt, Yvik Swan
We use Stein characterisations to derive new moment-type estimators for the parameters of several truncated multivariate distributions in the i.i.d. case; we also derive the asympt…
One step futher: an explicit solution to Robbins' problem when
Rémi Dendievel, Yvik Swan
Fix some and let be independent random variables drawn from the uniform distribution on . A decision maker is shown the variables se…
Stein's Method of Moments on the Sphere
Adrian Fischer, Robert E. Gaunt, Yvik Swan
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,…
IT formulae for gamma target: mutual information and relative entropy
Benjamin Arras, Yvik Swan
In this paper, we introduce new Stein identities for gamma target distribution as well as a new non-linear channel specifically designed for gamma inputs. From these two ingredient…
First order covariance inequalities via Stein's method
Marie Ernst, Gesine Reinert, Yvik Swan
We propose probabilistic representations for inverse Stein operators (i.e. solutions to Stein equations) under general conditions; in particular we deduce new simple expressions fo…
Maximum likelihood characterization of distributions
Mitia Duerinckx, Christophe Ley, Yvik Swan
A famous characterization theorem due to C.F. Gauss states that the maximum likelihood estimator (MLE) of the parameter in a location family is the sample mean for all samples of a…
Stein's method, many interacting worlds and quantum mechanics
Ian W. McKeague, Erol A. Peköz, Yvik Swan
Hall, Deckert and Wiseman (2014) recently proposed that quantum theory can be understood as the continuum limit of a deterministic theory in which there is a large, but finite, num…
Regularity of solutions of the Stein equation and rates in the multivariate central limit theorem
Thomas Gallouët, Guillaume Mijoule, Yvik Swan
Consider the multivariate Stein equation , where is a standard -dimensional Gaussian random vector, and let be the solution giv…
Distances between distributions via Stein's method
Marie Ernst, Yvik Swan
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 s…
Simple variance bounds with applications to Bayesian posteriors and intractable distributions
Fraser Daly, Fatemeh Ghaderinezhad, Christophe Ley +1
Using coupling techniques based on Stein's method for probability approximation, we revisit classical variance bounding inequalities of Chernoff, Cacoullos, Chen and Klaassen. Taki…
Stein-type covariance identities: Klaassen, Papathanasiou and Olkin-Shepp type bounds for arbitrary target distributions
Marie Ernst, Gesine Reinert, Yvik Swan
In this paper, we present a minimal formalism for Stein operators which leads to different probabilistic representations of solutions to Stein equations. These in turn provide a wi…
A remark on the ARE between Wilcoxon's and van~der~Waerden's scores
Nadir Maaroufi, Camille Sabbah, Yvik Swan +1
This paper is concerned with a comparison of van der Waerden's and Wilcoxon's scores.
A Stochastic Analysis of some Two-Person Sports
Davy Paindaveine, Yvik Swan
We consider two-person sports where each rally is initiated by a \emph{server}, the other player (the \emph{receiver}) becoming the server when he/she wins a rally. Historically, t…
Independent additive weighted bias distributions and associated goodness-of-fit tests
Bruno Ebner, Yvik Swan
We use a Stein identity to define a new class of parametric distributions which we call ``independent additive weighted bias distributions.'' We investigate related -type disc…
A unified approach to Stein characterizations
Christophe Ley, Yvik Swan
This article deals with Stein characterizations of probability distributions. We provide a general framework for interpreting these in terms of the parameters of the underlying dis…
Normal approximation for the posterior in exponential families
Adrian Fischer, Robert E. Gaunt, Gesine Reinert +1
In this paper, we obtain quantitative, non-asymptotic, and data-dependent \textit{Bernstein-von Mises type} bounds on the normal approximation of the posterior distribution in expo…
Stein's method for Fréchet approximation: a regularly varying functions approach
Paul Mansanarez, Guillaume Poly, Yvik Swan
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…
Stein's density method for multivariate continuous distributions
Guillaume Mijoule, Martin RaiÄ, Gesine Reinert +1
This paper provides a general framework for Stein's density method for multivariate continuous distributions. The approach associates to any probability density function a canonica…
On infinite covariance expansions
Marie Ernst, Gesine Reinert, Yvik Swan
In this paper we provide a probabilistic representation of Lagrange's identity which we use to obtain Papathanasiou-type variance expansions of arbitrary order. Our expansions lead…
A Stochastic Analysis of Table Tennis
Yves Dominicy, Christophe Ley, Yvik Swan
We establish a general formula for the distribution of the score in table tennis. We use this formula to derive the probability distribution (and hence the expectation and variance…
Stein's Method Meets Computational Statistics: A Review of Some Recent Developments
Andreas Anastasiou, Alessandro Barp, François-Xavier Briol +11
Stein's method compares probability distributions through the study of a class of linear operators called Stein operators. While mainly studied in probability and used to underpin…