Related papers: A doubly composite Chernoff-Stein lemma and its ap…

Let $X, X_1, X_2,\ldots $ be a sequence of non-lattice i.i.d. random variables with ${\bf E} X=0,$ ${\bf E} X=1,$ and let $S_n:= X_1+ \cdots+ X_n$, $n\ge 1.$ We refine Stone's integro-local theorem by deriving the first term in the…

Two-sample inference for the difference of population means typically relies upon a Central Limit Theorem approximation. When data are drawn from a Negative Binomial distribution, previous work of Shilane et al. (2010) showed that a Normal…

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…

The direct part of Stein's lemma in quantum hypothesis testing is revisited based on a key operator inequality between a density operator and its pinching. The operator inequality is used to show a simple proof of the direct part of Stein's…

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…

We consider the sequential composite binary hypothesis testing problem in which one of the hypotheses is governed by a single distribution while the other is governed by a family of distributions whose parameters belong to a known set…

Chung's Lemma is a classical tool for establishing asymptotic convergence rates of (stochastic) optimization methods under strong convexity-type assumptions and appropriate polynomial diminishing step sizes. In this work, we develop a…

Complementarity relations between various characterizations of a probability distribution are at the core of information theory. In particular, lower and upper bounds for the entropic function are of great importance. In applied topics, we…

We develop a multidimensional Stein methodology for non-degenerate self-decomposable random vectors in $\mathbb{R}^d$ having finite first moment. Building on previous univariate findings, we solve an integro-partial differential Stein…

We address the problem of image denoising in additive white noise without placing restrictive assumptions on its statistical distribution. In the recent literature, specific noise distributions have been considered and correspondingly,…

We investigate the ability of a quantum measurement device to discriminate two states or, generically, two hypothesis. In full generality, the measurement can be performed a number $n$ of times, and arbitrary pre-processing of the states…

We propose a Stein characterization of the Kummer distribution on (0, $\infty$). This result follows from our observation that the density of the Kummer distribution satisfies a certain differential equation, leading to a solution of the…

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…

This work is devoted to explore fundamental aspects of the spectral properties of few-body general operators. We first consider the following question: when we know the probability distributions of a set of observables, what can we way on…

We establish existence of Stein kernels for probability measures on $\mathbb{R}^d$ satisfying a Poincar\'e inequality, and obtain bounds on the Stein discrepancy of such measures. Applications to quantitative central limit theorems are…

The max-relative entropy and the conditional min-entropy it induces have become central to one-shot information theory. Both may be expressed in terms of a conic program over the positive semidefinite cone. Recently, it was shown that the…

We provide a new perspective on Stein's so-called density approach by introducing a new operator and characterizing class which are valid for a much wider family of probability distributions on the real line. We prove an elementary…

Stein's (1959) problem highlights the phenomenon called the probability dilution in high dimensional cases, which is known as a fundamental deficiency in probabilistic inference. The satellite conjunction problem also suffers from…

Let F ($\nu$) be the centered Gamma law with parameter $\nu$ > 0 and let us denote by P Y the probability distribution of a random vector Y. We develop a multidimensional variant of the Stein's method for Gamma approximation that allows to…

The law of likelihood underlies a general framework, known as the likelihood paradigm, for representing and interpreting statistical evidence. As stated, the law applies only to simple hypotheses, and there have been reservations about…