Related papers: On Stein's method for multivariate normal approxim…
Many spatial models exhibit locality structures that effectively reduce their intrinsic dimensionality, enabling efficient approximation and sampling of high-dimensional distributions. However, existing approximation techniques primarily…
In many applications, we encounter data on Riemannian manifolds such as torus and rotation groups. Standard statistical procedures for multivariate data are not applicable to such data. In this study, we develop goodness-of-fit testing and…
It is known that the fluctuations of suitable linear statistics of Haar distributed elements of the compact classical groups satisfy a central limit theorem. We show that if the corresponding test functions are sufficiently smooth, a rate…
Stein's method (Stein, 1973; 1981) is a powerful tool for statistical applications and has significantly impacted machine learning. Stein's lemma plays an essential role in Stein's method. Previous applications of Stein's lemma either…
We obtain rates of convergence in limit theorems of partial sums $S_n$ for certain sequences of dependent, identically distributed random variables, which arise naturally in statistical mechanics, in particular, in the context of the…
We consider the problem of efficiently computing the maximum likelihood estimator in Generalized Linear Models (GLMs) when the number of observations is much larger than the number of coefficients ($n \gg p \gg 1$). In this regime,…
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…
Generalized additive models have been popular among statisticians and data analysts in multivariate nonparametric regression with non-Gaussian responses including binary and count data. In this paper, a new likelihood approach for fitting…
Stein's paradox holds considerable sway in high-dimensional statistics, highlighting that the sample mean, traditionally considered the de facto estimator, might not be the most efficacious in higher dimensions. To address this, the…
We provide a sharp nonasymptotic analysis of the rates of convergence for some standard multivariate Markov chains using spectral techniques. All chains under consideration have multivariate orthogonal polynomial as eigenfunctions. Our…
We obtain explicit Berry-Esseen bounds in the Kolmogorov distance for the normal approximation of non-linear functionals of vectors of independent random variables. Our results are based on the use of Stein's method and of random difference…
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 result of Gaunt, Mijoule and Swan \cite{gms18}. This…
Stochastic variance reduction algorithms have recently become popular for minimizing the average of a large, but finite number of loss functions. The present paper proposes a Riemannian stochastic quasi-Newton algorithm with variance…
We establish presumably optimal rates of normal convergence with respect to the Kolmogorov distance for a large class of geometric functionals of marked Poisson and binomial point processes on general metric spaces. The rates are valid…
For parameter estimation of continuous and discrete distributions, we propose a generalization of the method of moments (MM), where Stein identities are utilized for improved estimation performance. The construction of these Stein-type…
Optimization with orthogonality constraints frequently arises in various fields such as machine learning. Riemannian optimization offers a powerful framework for solving these problems by equipping the constraint set with a Riemannian…
This work introduces a new, explicit bound on the Hellinger distance between a continuous random variable and a Gaussian with matching mean and variance. As example applications, we derive a quantitative Hellinger central limit theorem and…
This review traces the evolution of theory that started when Charles Stein in 1955 [In Proc. 3rd Berkeley Sympos. Math. Statist. Probab. I (1956) 197--206, Univ. California Press] showed that using each separate sample mean from $k\ge3$…
This survey article discusses the main concepts and techniques of Stein's method for distributional approximation by the normal, Poisson, exponential, and geometric distributions, and also its relation to concentration inequalities. The…
The paper applies the theory developed in Part I to the discrete normal approximation in total variation of random vectors in ${\mathbb Z}^d$. We illustrate the use of the method for sums of independent integer valued random vectors, and…