Related papers: On Stein's Method for Multivariate Self-Decomposab…
Over the last 80 years there has been much interest in the problem of finding an explicit formula for the probability density function of two zero mean correlated normal random variables. Motivated by this historical interest, we use a…
Stein variational gradient descent (SVGD) is a kernel-based and non-parametric particle method for sampling from a target distribution, such as in Bayesian inference and other machine learning tasks. Different from other particle methods,…
Stein's formula states that a random variable of the form $z^\top f(z) - \text{div} f(z)$ is mean-zero for functions $f$ with integrable gradient. Here, $\text{div} f$ is the divergence of the function $f$ and $z$ is a standard normal…
Kernel discrepancies are a powerful tool for analyzing worst-case errors in quasi-Monte Carlo (QMC) methods. Building on recent advances in optimizing such discrepancy measures, we extend the subset selection problem to the setting of…
Distances between probability distributions that take into account the geometry of their sample space,like the Wasserstein or the Maximum Mean Discrepancy (MMD) distances have received a lot of attention in machine learning as they can, for…
We study the estimation of the parametric components of single and multiple index volatility models. Using the first- and second-order Stein's identities, we develop methods that are applicable for the estimation of the variance index in…
The author uses a Stein-type covariance identity to obtain moment estimators for the parameters of the quadratic polynomial subfamily of Pearson distributions. The asymptotic distribution of the estimators is obtained, and normality and…
Bayesian inference for doubly intractable distributions is challenging because they include intractable terms, which are functions of parameters of interest. Although several alternatives have been developed for such models, they are…
Dynamic discrete choice models often discretize the state vector and restrict its dimension in order to achieve valid inference. I propose a novel two-stage estimator for the set-identified structural parameter that incorporates a…
Given a random variable $F$ regular enough in the sense of the Malliavin calculus, we are able to measure the distance between its law and almost any continuous probability law on the real line. The bounds are given in terms of the…
We develop a new formulation of Stein's method to obtain computable upper bounds on the total variation distance between the geometric distribution and a distribution of interest. Our framework reduces the problem to the construction of a…
In this paper, we present a technically simple method to establish upper bounds on the expected injective norm of real and complex random tensors. Our approach is somewhat analogous to the moment method in random matrix theory, and is based…
We study the weighted Poincar\'e constant $C(p,w)$ of a probability density $p$ with weight function $w$ using integration methods inspired by Stein's method. We obtain a new version of the Chen-Wang variational formula which, as a…
Using Stein's method techniques, we develop a framework which allows one to bound the error terms arising from approximation by the Laplace distribution and apply it to the study of random sums of mean zero random variables. As a corollary,…
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…
Using a characterizing equation for the Beta distribution, Stein's method is applied to obtain bounds of the optimal order for the Wasserstein distance between the distribution of the scaled number of white balls drawn from a…
Optimal transport has been very successful for various machine learning tasks; however, it is known to suffer from the curse of dimensionality. Hence, dimensionality reduction is desirable when applied to high-dimensional data with…
Stein's method is used to approximate sums of discrete and locally dependent random variables by a centered and symmetric Binomial distribution. Under appropriate smoothness properties of the summands, the same order of accuracy as in the…
A crucial task in predictive maintenance is estimating the remaining useful life of physical systems. In the last decade, deep learning has improved considerably upon traditional model-based and statistical approaches in terms of predictive…
In this paper we use a Malliavin-Stein type method to investigate Poisson and normal approximations for the measurable functions of infinitely many independent random variables. We combine Stein's method with the difference operators in…