Related papers: Bounding Hellinger Distance with Stein's Method
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…
This article derives quantitative limit theorems for multivariate Poisson and Poisson process approximations. Employing the solution of Stein's equation for Poisson random variables, we obtain an explicit bound for the multivariate Poisson…
In this paper, we establish optimal Berry--Esseen bounds for the generalized $U$-statistics. The proof is based on a new Berry--Esseen theorem for exchangeable pair approach by Stein's method under a general linearity condition setting. As…
In this article, we first obtain, for the Kolmogorov distance, an error bound between a tempered stable and a compound Poisson distribution and also an error bound between a tempered stable and an alpha stable distribution via Stein method.…
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…
A parametric theory of statistical inference is developed for the moderate deviation probability zone. The new approach to the proofs is based on the Taylor series expansion of the logarithm of the likelihood ratio based on the Hellinger…
Stein's method is applied to obtain a general Cramer-type moderate deviation result for dependent random variables whose dependence is defined in terms of a Stein identity. A corollary for zero-bias coupling is deduced. The result is also…
In Part I of this article (Banerjee and Kuchibhotla (2023)), we have introduced a new method to bound the difference in expectations of an average of independent random vector and the limiting Gaussian random vector using level sets. In the…
New bounds for the $k$-th order derivatives of the solutions of the normal and multivariate normal Stein equations are obtained. Our general order bounds involve fewer derivatives of the test function than those in the existing literature.…
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…
We obtain almost optimal convergence rate in the central limit theorem for "nonconevntional" sums of the form $S_N=N^{-\frac12}\sum_{n=1}^N (F(\xi_n,\xi_{2n},...,\xi_{\ell n})-\bar F)$.
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…
The first part of this work 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…
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…
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…
The study of the normalized sum of random variables and its asymptotic behaviour has been and continues to be a central chapter in probability and statistical mechanics. When those variables are independent the central limit theorem ensures…
In this article, we discuss the basic ideas of a general procedure to adapt the Stein-Chen method to bound the distance between conditional distributions. From an integration-by-parts formula (IBPF), we derive a Stein operator whose…
A classical statistical inequality is used to show that the distance covariance of two bounded random vectors is bounded from above by a simple function of the dimensionality and the bounds of the random vectors. Two special cases that…
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…
We consider the optimal transport problem between multivariate Gaussian stationary stochastic processes. The transportation effort is the variance of the filtered discrepancy process. The main contribution of this technical note is to show…