Related papers: From Stein identities to moderate deviations
We present a way to use Stein's method in order to bound the Wasserstein distance of order $2$ between two measures $\nu$ and $\mu$ supported on $\mathbb{R}^d$ such that $\mu$ is the reversible measure of a diffusion process. In order to…
We study conditions under which treatment effect estimators constructed under the no-interference assumption in randomized experiments are asymptotically normal in the presence of interference. We prove that the standard Horvitz-Thompson…
We derive a large deviation principle for families of random variables in the basin of attraction of spectrally positive stable distributions by proving a uniform version of the Tauberian theorem for Laplace-Stieltjes transforms. The main…
This paper concerns the development of Stein's method for chi-square approximation and its application to problems in statistics. New bounds for the derivatives of the solution of the gamma Stein equation are obtained. These bounds involve…
A moderate deviation principle as well as moderate and large deviation inequalities for a sequence of elements living inside a fixed Wiener chaos associated with an isonormal Gaussian process are shown. The conditions under which the…
We use a multivariate version of Stein's method to establish a quantitative Lindeberg CLT for the Fourier transforms of random $N$-vectors. We achieve this by deducing a specific integral representation for the Hessian matrix of a solution…
We take another look at using Stein's method to establish uniform Berry-Esseen bounds for Studentized nonlinear statistics, highlighting variable censoring and an exponential randomized concentration inequality for a sum of censored…
Gradient-based approximate inference methods, such as Stein variational gradient descent (SVGD), provide simple and general-purpose inference engines for differentiable continuous distributions. However, existing forms of SVGD cannot be…
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 discuss spin models on complete graphs in the mean-field (infinite-vertex) limit, especially the classical XY model, the Toy model of the Higgs sector, and related generalizations. We present a number of results coming from the theory of…
Testing conditional independence has many applications, such as in Bayesian network learning and causal discovery. Different test methods have been proposed. However, existing methods generally can not work when only discretized…
The K-sample testing problem involves determining whether K groups of data points are each drawn from the same distribution. Analysis of variance is arguably the most classical method to test mean differences, along with several recent…
We establish a quantitative normal approximation result for sums of random variables with multilevel local dependencies. As a corollary, we obtain a quantitative normal approximation result for linear functionals of random fields which may…
For an absolutely continuous (integer-valued) r.v. $X$ of the Pearson (Ord) family, we show that, under natural moment conditions, a Stein-type covariance identity of order $k$ holds (cf. [Goldstein and Reinert, J. Theoret. Probab. 18…
To improve the efficiency of Monte Carlo estimation, practitioners are turning to biased Markov chain Monte Carlo procedures that trade off asymptotic exactness for computational speed. The reasoning is sound: a reduction in variance due to…
Using Chen-Stein method in combination with size-biased couplings, we obtain the multivariate Poisson approximation in terms of the Wasserstein distance. As applications, we study the multivariate Poisson approximation of the distribution…
This paper is a short exposition of Stein's method of normal approximation from my personal perspective. It focuses mainly on the characterization of the normal distribution and the construction of Stein identities. Through examples, it…
This paper establishes a non-uniform Berry--Esseen bound for non-normal approximation using Stein's method. The main theorem generalizes the result of the authors in [Comptes Rendus Mathematique, 2024] to the context of non-normal…
Knowing the error distribution is important in many multivariate time series applications. To alleviate the risk of error distribution mis-specification, testing methodologies are needed to detect whether the chosen error distribution is…
In this paper we establish a multivariate exchangeable pairs approach within the framework of Stein's method to assess distributional distances to potentially singular multivariate normal distributions. By extending the statistics into a…