Related papers: First order covariance inequalities via Stein's me…
The upper bound inequality for variance of weighted sum of correlated random variables is derived according to Cauchy-Schwarz's inequality, while the weights are non-negative with sum of 1. We also give a novel proof with positive…
We consider random matrices that have invariance properties under the action of unitary groups (either a left-right invariance, or a conjugacy invariance), and we give formulas for moments in terms of functions of eigenvalues. Our main tool…
Stein's method for measuring convergence to a continuous target distribution relies on an operator characterizing the target and Stein factor bounds on the solutions of an associated differential equation. While such operators and bounds…
We will establish the connection between the Lorentz covariant and so-called single-time formulation for the quark Wigner operator. To this end we will discuss the initial value problem for the Wigner operator of a field theory and give a…
In this article, we present the theoretical basis for an approach to Stein's method for probability distributions on Riemannian manifolds. Using a semigroup representation for the solution to the Stein equation, we use tools from stochastic…
In this paper we obtain non-uniform Berry-Esseen bounds for normal approximations by the Malliavin-Stein method. The techniques rely on a detailed analysis of the solutions of Stein's equations and will be applied to functionals of a…
In this paper, we characterize the sharp constant and maximizing functions for weighted Poincar\'e inequalities. These results lead to refinements of Hardy's inequality obtained by adding remainder terms involving \(L^p\) norms. We use…
A Steiner type formula for continuous translation invariant Minkowski valuations is established. In combination with a recent result on the symmetry of rigid motion invariant homogeneous bivaluations, this new Steiner type formula is used…
Let $Z$ be a standard normal random variable and let $H_n$ denote the $n$-th Hermite polynomial. In this note, we obtain Stein equations for the random variables $H_3(Z)$ and $H_4(Z)$, which represents a first step towards developing…
Covariance estimation and selection for multivariate datasets in a high-dimensional regime is a fundamental problem in modern statistics. Gaussian graphical models are a popular class of models used for this purpose. Current Bayesian…
Stein kernels are a way of comparing probability distributions, defined via integration by parts formulas. We provide two constructions of Stein kernels in free probability. One is given by an explicit formula, and the other via free…
The Schr{\"o}dinger inequality is known to underlie the Kennard-Robertson inequality, which is the standard expression of quantum uncertainty for the product of variances of two observables $A$ and $B$, in the sense that the latter is…
We present an alternative way of solving the steerable kernel constraint that appears in the design of steerable equivariant convolutional neural networks. We find explicit real and complex bases which are ready to use, for different…
We prove lower bounds on the number of samples needed to privately estimate the covariance matrix of a Gaussian distribution. Our bounds match existing upper bounds in the widest known setting of parameters. Our analysis relies on the…
The Covariant Spectator Theory (CST) is used to calculate the mass spectrum and vertex functions of heavy-light and heavy mesons in Minkowski space. The covariant kernel contains Lorentz scalar, pseudoscalar, and vector contributions. The…
This paper focuses on investigating Stein's invariant shrinkage estimators for large sample covariance matrices and precision matrices in high-dimensional settings. We consider models that have nearly arbitrary population covariance…
We introduce the notion of {\em covariance measure structure} for square integrable stochastic processes. We define Wiener integral, we develop a suitable formalism for stochastic calculus of variations and we make Gaussian assumptions only…
Using coupling techniques based on Stein's method for probability approximation, we revisit classical variance bounding inequalities of Chernoff, Cacoullos, Chen and Klaassen. Taking advantage of modern coupling techniques allows us to…
We establish explicit bounds on the convex distance between the distribution of a vector of smooth functionals of a Gaussian field, and that of a normal vector with a positive definite covariance matrix. Our bounds are commensurate to the…
In this article, we establish a general covariance identity for infinitely divisible distributions (IDD). Using this result, we derive Cacoullos type variance bounds for the IDD. Applications to some important distributions are discussed,…