Related papers: Version-Robust Methods for Identifying Minimal Suf…

We give a sharp lower bound on the capacity of a real stable polynomial, depending only on the value of its gradient at $x = 1$. This result implies a sharp improvement to a similar inequality proved by Linial-Samorodnitsky-Wigderson in…

We derive a simple sufficient condition for the local asymptotic stability of spatially discrete, continuous-time reaction-diffusion systems of networked dynamical systems at a homogeneous equilibrium point. The framework explicitly…

An important tool to quantify the likeness of two probability measures are f-divergences, which have seen widespread application in statistics and information theory. An example is the total variation, which plays an exceptional role among…

We develop new techniques for proving lower bounds on the least singular value of random matrices with limited randomness. The matrices we consider have entries that are given by polynomials of a few underlying base random variables. This…

Since the two seminal papers by Fisher (1915, 1921) were published, the test under a fixed value correlation coefficient null hypothesis for the bivariate normal distribution constitutes an important statistical problem. In the framework of…

This paper aims first at a simultaneous axiomatic presentation of the proof of optimal convergence rates for adaptive finite element methods and second at some refinements of particular questions like the avoidance of (discrete) lower…

We consider the distributed detection problem of a temporally correlated random radio source signal using a wireless sensor network capable of measuring the energy of the received signals. It is well-known that optimal tests in the…

In the regression discontinuity design (RDD), it is common practice to assess the credibility of the design by testing the continuity of the density of the running variable at the cut-off, e.g., McCrary (2008). In this paper we propose an…

Using the ordinal pattern concept in permutation entropy, we propose a model sufficiency test to study a given model's point prediction accuracy. Compared to some classical model sufficiency tests, such as the Broock et al.'s (1996) test,…

In scientific inference problems, the underlying statistical modeling assumptions have a crucial impact on the end results. There exist, however, only a few automatic means for validating these fundamental modelling assumptions. The…

We prove an existence theorem for the sliding boundary variant of the Plateau problem for $2$-dimensional sets in $\mathbb{R}^n$. The simplest case of sufficient condition is when $n=3$ and the boundary $\Gamma$ is a finite disjoint union…

This paper presents a new general formulation of the Radon-Nikodym theorem in the setting of abstract measure theory. We introduce the notion of weak localizability for a measure and show that this property is both necessary and sufficient…

We study linear subset regression in the context of the high-dimensional overall model $y = \vartheta+\theta' z + \epsilon$ with univariate response $y$ and a $d$-vector of random regressors $z$, independent of $\epsilon$. Here,…

Score-based diffusion models, while achieving minimax optimality for sampling, are often hampered by slow sampling speeds due to the high computational burden of score function evaluations. Despite the recent remarkable empirical advances…

In this article, we revisit the question of fluctuations of linear statistics of beta ensembles in the single cut and non-critical regime for general potentials $V$ under mild regularity and growth assumptions. Our main objective is to…

This paper considers the estimation of Shannon entropy for discrete distributions with countably infinite support. While minimax rates for finite-support distributions are established, infinite-support distributions present distinct…

It is known that if a 2-universal hash function $H$ is applied to elements of a {\em block source} $(X_1,...,X_T)$, where each item $X_i$ has enough min-entropy conditioned on the previous items, then the output distribution…

Statistical sufficiency formalizes the notion of data reduction. In the decision theoretic interpretation, once a model is chosen all inferences should be based on a sufficient statistic. However, suppose we start with a set of procedures…

On an abstract Wiener space, assume that T is the solution of the quadratic Monge problem associated to the Wiener measure and a second one with a Radon-Nikodym derivative of exponential type. Under the finite information hypothesis, using…

We address combinatorial problems that can be formulated as minimization of a partially separable function of discrete variables (energy minimization in graphical models, weighted constraint satisfaction, pseudo-Boolean optimization, 0-1…